Praise be to Allah.
Welcome to a lady who is seeking the true religion and is interested in Islam. We ask Allaah to show you the truth and help you to follow it, and to protect you from Shaytaan and his doubts, and the misguidance of the enemies of Islam.
Before I answer your question, I would like to remind you that the way to find out the truth about a religion is to refer to its authentic sources, which in the case of Islam means the Quraan, which is the Word of Allaah, and the Sunnah, which is the words of the Prophet of Islam, Muhammad (peace and blessings of Allaah be upon him), to whom Allaah sent Revelation.
One of the mistakes made by some of those who investigate Islam is to refer to sources that are not authentic or material written by those who have ulterior motives and who are enemies of Islam spreading lies about it, to put people off and lead them astray from the Way of Allaah.
Turning to your question about the Kabah, and Ibraaheem and Ismaaeel (upon whom be peace), it is very strange to say that they removed all the idols from the Kabah except one. This contradicts the historical facts, and does not make sense, because it is known that Ibraaheem and Ismaaeel were the ones who built the Kabah, on the command of Allaah how could they then have taken idols out of it? How could there have been any idols in it when they were supervising its construction and maintenance by remembering Allaah and calling people to perform Tawaaf around it and come on pilgrimage to it only for the sake of Allaah? The idols came many years afterwards, when some of the Arabs travelled to the kaafir lands outside the Arabian Peninsula and brought back idols, some of which were placed around the Kabah. Then the mushrikeen added more idols until there were 360 of them around the Kabah. This remained the case until Allaah sent Muhammad (peace and blessings of Allaah be upon him). This was the dawning of the light of Tawheed which drove out the darkness of idolatry. Through him, Allaah defeated the mushrikeen; he broke the idols and purified the Sacred House, thus restoring the Kabah to the pure worship of the One God, as it had been at the time of his forefather Ibraaheem, the Friend (Khaleel) of Allaah.
There follows an account of the building of the Ancient House, from the Quraan and the Ahaadeeth of the Prophet (peace and blessings of Allaah be upon him). We will begin by quoting from the Quraan, where Allaah says (interpretation of the meaning):
"And (remember) when Ibraaheem said: My Lord, make this city (Makkah) a place of security and provide its people with fruits, such of them as believe in Allaah and the Last Day. He (Allaah) answered, As for him who disbelieves, I shall leave him in contentment for a while, then I shall compel him to the torment of the Fire, and worst indeed is that destination!
And (remember) when Ibraaheem and (his son) Ismaaeel were raising the foundations of the House (the Kabah), (saying): Our Lord! Accept (this service) from us. Verily! You are the All-Hearer, the All-Knower.
Our Lord! And make us submissive unto You and of our offspring a nation submissive unto You, and show us our manaasik (all the ceremonies of pilgrimage Hajj and Umrah), and accept our repentance. Truly, You are the One Who accepts repentance, the Most Merciful.
Our Lord! Send amongst them a Messenger of their own, who shall recite unto them Your Verses and instruct them in the Book and al-Hikmah (full knowledge of the Islamic laws and jurisprudence or wisdom or Prophethood, etc.), and sanctify them. Verily, You are the All-Mighty, the All-Wise."
"And (remember) when We showed Ibraaheem the site of the (Sacred) House, (saying): Associate not anything (in worship) with Me, and sanctify My House for those who circumambulate it, and those who stand up for prayer, and those who bow (submit themselves with humility and obedience to Allaah), and make prostration (in prayer, etc.)
And proclaim to mankind the Hajj (pilgrimage). They will come to you on foot and on every lean camel, they will come from every deep and distant (wide) mountain highway (to perform Hajj)."
As regards the story of the construction of the Kabah in the Sunnah, Ibn Abbaas (may Allaah be pleased with him) narrated the story of Haajar, the wife of Ibraaheem and the mother of his son Ismaaeel. In his report, he said:
" Ibraaheem brought her and her son Ismaaeel, while she was still breast-feeding him, and left them in a place near the Kabah (meaning near the place where the Kabah was later built) under a tree on the spot of Zamzam (meaning the place where Zamzam later appeared), at the highest place in the mosque. In those days there was no-one in Makkah nor was there any water. So he left them there and placed near them a leather bag containing some dates, and a water-skin containing some water, then he set off for home. Ismaaeels mother followed him and said: O Ibraaheem, where are you going, leaving us in this valley where there is no person whose company we may enjoy, nor is there anything (to enjoy)? She said this many times, but he did not look back at her. Then she asked him, Has Allaah commanded you to do this? He said, Yes. She said, Then He will not forsake us, and returned, while Ibraaheem went on his way. When he reached al-Thaaniyah, where they could not see him, he turned to face the Kabah, raised his hands and offered the supplication: O Our Lord! I have made some of my offspring dwell in an uncultivable valley, by Your Sacred House in order, O Our Lord, that they may perform al-Salaat (iqaamat al-salaat), so fill some hearts among men with love towards them, and (O Allaah) provide them with fruits so that they may give thanks. [Ibraaheem 14:37]
Ismaaeels mother went on suckling Ismaaeel and drinking from the water (she had). When the water in the water-skin had all been used up, she became thirsty and her child also became thirsty. She started looking at him tossing in agony; she left him because she could not endure looking at him, and found that the mountain of al-Safaa was the nearest mountain to her on that land. She stood on it and started looking at the valley keenly so that she might see somebody, but she could not see anybody. Then she descended from al-Safaa and when she reached the valley, she tucked up her robe and ran in the valley like a person in distress and trouble, till she crossed the valley and reached the mountain of al-Marwa, where she stood and started looking, expecting to see somebody, but she could not see anybody. She repeated that (running between al-Safaa and al-Marwa) seven times." Ibn Abbaas said: "The Prophet (peace and blessings of Allaah be upon him) said: This is the origin of the tradition of al-Saee (the walking) of people between them (al-Safaa and al-Marwa). When she reached al-Marwa (for the last time), she heard a voice and she made herself quiet and listened attentively. She heard the voice again and said, O (whoever you may be)! You have made me hear your voice; have you got something to help me? And behold! She saw an angel at the place of Zamzam, digging the earth with his heel (or his wing), till water flowed from that place. She started to make something like a basin around it, using her hands in this way, and started filling her water-skin with water from her hands, and the water was flowing out after she had scooped some of it." The Prophet (peace and blessings of Allaah be upon him) added: "May Allaah bestow mercy on Ismaaeels mother! Had she let the Zamzam (flow without trying to control it) (or had she not scooped from that water) (to fill her water-skin), Zamzam would have been a stream flowing on the surface of the earth." The Prophet (peace and blessings of Allaah be upon him) further added: "Then she drank (water) and suckled her child. The angels said to her: Dont be afraid of being forsaken, for this is the House of Allaah which will be built by this boy and his father, and Allaah never forsakes His people. The House at that time was on a high place resembling a hillock, and when torrents came, they flowed to its right and left. She lived in that way until some people from the tribe of Jurhum or a family from Jurhum passed by her and her child, as they (the Jurhum people) were coming through the way of Kadaa. They stopped and stayed in the lower part of Makkah where they saw a bird that had the habit of flying around water and not leaving it. They said, This bird must be flying around water, although we know that there is no water in this valley. They sent one or two messengers who discovered the source of water, and returned to inform them about it. So, they all came (towards the water)." The Prophet (peace and blessings of Allaah be upon him) added: "Ismaaeels mother was sitting near the water. They asked her, Do you allow us to stay with you? She replied, Yes, but you will have no right to possess the water. They agreed to that." The Prophet (peace and blessings of Allaah be upon him) further added: "Ismaaeels mother was pleased with the whole situation, as she used to love to enjoy the company of the people. So, they settled there, and later on they sent for their families who came and settled with them so that some families became permanent residents there. The child (Ismaaeel) grew up and learnt Arabic from them, and (his virtues) caused them to love and admire him as he grew up. When he reached the age of puberty, they made him marry a woman from amongst them. After Ismaaeels mother had died, Ibraaheem came after Ismaaeels marriage in order to see his family that he had left before Then Ibraaheem came and saw Ismaaeel under a tree near Zamzam, sharpening his arrows. When he saw Ibraaheem, he stood up to welcome him and they greeted one another as a father greets his son or a son greets his father. Ibraaheem said, O Ismaaeel, Allaah has given me an order. Ismaaeel said: Do what your Lord has ordered you to do. Ibraaheem asked, Will you help me? Ismaaeel said, I will help you. Ibraaheem said, Allaah has ordered me to build a house here, pointing to a hillock higher than the land surrounding it." The Prophet (peace and blessings of Allaah be upon him) added: "Then they raised the foundations of the House (Kabah). Ismaaeel brought the stones and Ibraaheem was building, and when the walls became high, Ismaaeel brought this stone and put it for Ibraaheem, who stood on it and carried on building, while Ismaaeel was handing him the stones, and both of them were saying: Our Lord! Accept (this service) from us. Verily! You are the All-Hearer, the All-Knower. [al-Baqarah 2:127]. The Prophet (peace and blessings of Allaah be upon him) added, "Then both of them went on building and going around the Kabah saying, Our Lord! Accept (this service) from us. Verily! You are the All-Hearer, the All-Knower." (Saheeh al-Bukhaari, 3113)
Having outlined the historical details of the building of the Kabah, we move on to the idea mentioned in your question that the name of Allaah was derived from the name of an idol. This is an extremely odd idea. How can the name of the Creator, the Evolver, the First, the Almighty, the Compellor be derived from the name of a created idol that could neither benefit nor harm anyone?
Allaah says, rebuking the mushrikeen (polytheists) (interpretation of the meaning): "Yet they have taken besides Him other gods that created nothing but are themselves created, and possess neither hurt nor benefit for themselves, and possess no power (of causing) death, nor (of giving) life, nor of raising the dead." [al-Furqaan 25:3]
"You worship besides Allaah only idols, and you only invent falsehood. Verily, those whom you worship besides Allaah have no power to give you provision, so seek your provision from Allaah (Alone), and worship Him (Alone), and be grateful to Him. To Him (Alone) you will be brought back." [al-Ankaboot 29:17]
Allaah describes how Ibraaheem (upon whom be peace) rebuked his father and his people for worshipping idols (interpretation of the meaning):
"When he said to his father: O my father! Why do you worship that which hears not, sees not and cannot avail you in anything?" [Maryam 19:42]
"And recite to them the story of Ibraaheem, when he said to his father and his people: What do you worship? They said: We worship idols, and to them we are ever devoted. He said, Do they hear you, when you call (on them)? Or do they benefit you or do they harm (you)? They said, Nay, but we found our fathers doing so. He said, Do you observe that which you have been worshipping, - you and your ancient fathers? Verily! They are enemies to me, save the Lord of the Aalameen (makind, jinn and everything that exists), Who has created me, and it is He Who guides me." [Al-Shuaraa 26:69-78]
Concerning Ibraaheems destruction of his peoples idols, Allaah says (interpretation of the meaning):
"Then he turned to their gods and said, Will you not eat (of the offering before you)? What is the matter with you that you speak not? Then he turned upon them, striking (them) with (his) right hand. Then they (the worshippers of idols) came towards him, hastening. He said, Worship you that which you (yourselves) carve? While Allaah has created you and what you make?" [al-Saaffaat 37:91-96]
After reading all this, how can it be said that Ibraaheem left one idol near the Kabah, and that the name of Allaah is derived from the name of an idol? Do you know what "Allaah" means and where this name is derived from?
The blessed name "Allaah" is derived from the Arabic verb alaha/yalahu/malooh [the root of which is the three letters alif, laam, haa]. This verb includes the meaning of love as well as worship. Allaah, may He be glorified and exalted, is the One Who is loved, glorified and feared by the believers, and they put their hope in Him.
As regards to your last question, about whether Islam has anything to do with the worship of idols or heavenly bodies, this is a strange matter indeed. Islam proclaimed the absolute unity of Allaah (Tawheed) and taught that He Alone is to be worshipped, with no partners or associates. Islam came to fight idolatry and put an end to it, so how can it possibly be connected to idol-worship?
Perhaps you have read in the Quraan the story of the hoopoe who believed only in Allaah; he knew Who his Lord was, and denounced the worship of stars and planets. Allaah says, relating how His Prophet Sulaymaan (upon whom be peace) conveyed the story to the queen of Yemen at that time (interpretation of the meaning):
"[The hoopoe said] and I have come to you from Saba (Sheba) with true news. I found a woman ruling over them, and she has been given all things that could be possessed by any ruler of the earth, and she has a great throne. I found her and her people worshipping the sun instead of Allaah, and Shaytaan has made their deeds fair-seeming to them, and has barred them from (Allaahs) Way, so they have no guidance, so that they do not worship (prostrate before) Allaah, Who brings to light what is hidden in the heavens and the earth, and knows what you conceal and what you reveal. Allaah, none has the right to be worshipped but He, the Lord of the Supreme Throne!" [al-Naml 27:22-26]
There is also the story of how Ibraaheem rebuked his people for worshipping heavenly bodies, the sun and moon, which Allaah has told us in Soorat al-Anaam (the sixth soorah).
The fast of Ramadaan is not connected to the moon because we worship the moon, but because the Lord of the moon has made it a marker of time for us, by which we may organize our worship and other affairs. So we look for the new moon of Ramadaan so that we may worship Allaah Alone by fasting, and we look for the new moon of the following month to mark the end of this annual act of worship. We also look for the timings of Hajj and other acts of worship in a similar way.
We hope that this has helped you understand anything that was not clear to you before. Note that this is a serious issue, and it is not something to be taken lightly. The only religion with Allaah is Islam, which He has chosen for His slaves, and He will not accept any other religion. Come and join the religion of truth, and follow what your Lord has revealed.