Praise be to Allah.
You should praise Allaah for having guided you and brought you back to Him. You have to observe the fasts that Allaah has enjoined upon you, even if your father dislikes that, because there is no obedience to any created being if it involves disobedience towards the Creator.
You say that you feel ill and that you suffer from anaemia and allergies. In that case you have to refer to a trustworthy doctor and ask him whether fasting is harmful for you or not, and whether there is any hope of a recovery from this disease or not. If fasting will harm you because of this sickness, or will make the sickness worse, or delay recovery, or make it very hard for you to fast, then Allaah has made things easy for you and has allowed you not to fast. So you should not fast, and you should make up the days that you do not fast after you recover, in sha Allaah.
But if this sickness is ongoing and there is no hope of making up the fasts, then do not fast, and you have to feed one poor person for each day that you do not fast. See question no. 12488.
The father has to look after his family properly, and tell them to do what is enjoined upon them and not to do that which is forbidden. If he falls short in that then he is exposed to divine wrath and punishment. Allaah says (interpretation of the meaning):
“O you who believe! Ward off yourselves and your families against a Fire (Hell) whose fuel is men and stones, over which are (appointed) angels stern (and) severe, who disobey not, (from executing) the Commands they receive from Allaah, but do that which they are commanded”
The Prophet (peace and blessings of Allaah be upon him) said: “There is no person whom Allaah appoints in charge of others and he dies having betrayed his charges, but Allaah will forbid Paradise to him.” Narrated by al-Bukhaari, 6731; Muslim, 142.
And the Prophet (peace and blessings of Allaah be upon him) said: “Each of you is a shepherd and is responsible for his flock… The man is the shepherd of his family and is responsible for his flock…” Narrated by al-Bukhaari, 844; Muslim, 3408. Each person who was in a position of authority and responsibility – including fathers – will be questioned as to whether he did what was required of him, or not?
It is well known that blessings and reward will result from this questioning, if he did what was required of him, and that he will deserve to be punished if he was careless and negligent. We ask Allaah to keep us safe and sound.
If the father’s negligence is compounded by his having forbidden his family to do good things or things that are obligatory, then his sin will be even greater. Allaah has told us that this is the characteristic of the hypocrites and evildoers, who enjoin evil and forbid good. He says (interpretation of the meaning):
“The hypocrites, men and women, are one from another; they enjoin (on the people) Al-Munkar (i.e. disbelief and polytheism of all kinds and all that Islam has forbidden), and forbid (people) from Al-Ma‘roof (i.e. Islamic Monotheism and all that Islam orders one to do), and they close their hands [from giving (spending in Allaah’s Cause) alms]. They have forgotten Allaah, so He has forgotten them. Verily, the hypocrites are the Faasiqoon (rebellious, disobedient to Allaah)”
You have to be patient and seek reward, and continue to advise your father. Seek the help of righteous people among your family and relatives in doing so, and pray for him to be guided aright.
You should beware of staying outside the home when there is no need, because of the harm and fitnah (temptation) that may result from that. If you need to go out, or are forced to do so, then you should observe correct shar’i hijaab. In question no. 6991 you can find out the conditions of correct shar’i hijaab.
We ask Allaah to protect You and to guide your father to the right way.
And Allaah knows best.