Praise be to Allah.
Before replying to this question, we must establish an important point about the virtues of certain soorahs.
There are fabricated ahaadeeth about the virtues of various soorahs which have been falsely attributed to the Messenger of Allaah (peace and blessings of Allaah be upon him). Among the most famous of those who are known for that are the following:
1 – Nooh ibn Abi Maryam al-Jaami’, of whom it was said: He encompassed everything except the truth. He regarded it as permissible to tell lies in hadeeth in the interests of the religion, and he made up ahaadeeth by himself and attributed them to the Messenger (peace and blessings of Allaah be upon him) concerning the virtues of the soorahs of the Qur’aan, soorah by soorah.
Abu ‘Ammaar al-Husayn ibn Hurayth al-Marwazi said: It was said to Abu ‘Ismah – i.e., Nooh ibn Abi Maryam - : “From where do you get (a hadeeth) from ‘Ikrimah from Ibn ‘Abbaas (may Allaah be pleased with him) concerning the virtues of the Qur’aan soorah by soorah, when the companions of ‘Ikrimah have no such hadeeth?” He said: “I saw that the people had turned away from the Qur’aan and were distracted by the fiqh of Abu Haneefah and the Maghaazi of Muhammad ibn Ishaaq, so I made up this hadeeth, seeing reward.”
Narrated by al-Haakim in al-Madkhal (p. 54); Ibn al-Jawzi in al-Mawdoo’aat (16). Its isnaad is saheeh.
2 – Maysarah ibn ‘Abd Rabbihi al-Faarisi, of whom Ibn Hibbaan said in al-Majrooheen (2/345, no. 1038): He is the author of a lengthy hadeeth about the virtues of the Qur’aan, in which it says: “Whoever recites such and such will have such and such.”
In Lisaan al-Meezaan (7/198) by al-Haafiz ibn Hajar it says: In al-Du’aafa’, Ibn Hibbaan narrated from Ibn Mahdi that he said: I said to Maysarah ibn ‘Abd Rabbihi: “From where did you get these ahaadeeth, ‘Whoever recites such and such will have such and such’?” He said: “I made them up in order to encourage the people.”
These are examples of people who made up false ahaadeeth and attributed them to the Messenger (peace and blessings of Allaah be upon him) for a purpose that they thought fit, by means of which Iblees deceived them.
The scholars drew attention to the fact that the ahaadeeth which list the virtues of all the soorahs of the Qur’aan soorah by soorah, are not proven. Among those who drew attention to that was al-Mawsili in al-Mughni ‘an al-Hifz wa’l-Kitaab (1/121). He said: And he narrated: “Whoever recites such and such will have such and such… from the beginning of the Qur’aan to the end. Ibn al-Mubaarak said: I think this was fabricated by the zindeeqs (heretics). The editor – i.e., al-Mawsili – said: There is no saheeh report concerning this.
Attention was also drawn to this by Ibn al-Qayyim in al-Manaar al-Muneef (p. 113-144) and Shaykh Bakr Abu Zayd in al-Tahdeeth bima qeela Laa yasahhu fihi hadeeth (p. 122-123). He added: It should be noted that the virtues of the Holy Qur’aan and the virtues of certain soorahs and verses are known from saheeh texts which are attributed to the Prophet (peace and blessings of Allaah be upon him). What Ibn al-Mubaarak and those who came after him meant was to discuss the lengthy ahaadeeth which discuss the soorahs of the Qur’aan soorah by soorah, such as the hadeeth which is attributed to Ubayy ibn Ka’b (may Allaah be pleased with him), which was quoted by some of the mufassireen – such as al-Tha’labi, al-Waahidi and al-Zamakhshari – in their Tafseers, which is fabricated. This is what is meant by the discussions of Ibn al-Mubaarak and others. And Allaah knows best. End quote.
With regard to the ahaadeeth that you asked about, the answer is as follows:
Source of the first hadeeth:
It was narrated that ‘Abd-Allaah ibn ‘Umar (may Allaah be pleased with him) said: The Messenger of Allaah (S) said: “Whoever reads ‘Alif‑Laam‑Meem. The revelation of the Book’ [al-Sajdah 32] and ‘Blessed be He in Whose Hand is the dominion’ [al-Mulk 67], between Maghrib and ‘Isha’, it is as if he spent Laylat al-Qadr in prayer.”
This was quoted by al-Suyooti in al-Durr al-Manthoor (6/535) at the beginning of Soorat al-Sajdah. He said: “Ibn Mardawayh narrated from Ibn ‘Umar …” and quoted it.
al-Aloosi quoted it in Rooh al-Ma’aani (21/116) from al-Suyooti, then he said: A similar report was narrated by him – meaning al-Suyooti – and al-Waahidi from the hadeeth of Ubayy ibn Ka’b, and by al-Tha’labi from the hadeeth of Ibn ‘Abbaas. Wali al-Deen commented on that by saying: “I do not agree with that; all of these reports are fabricated.” End quote.
Several versions of the hadeeth have been narrated, some of which are general in meaning and do not specify a time for reading, and some of which do specify a time, as in the report of Ibn ‘Umar. It has been narrated as marfoo’ and mawqoof. Al-Ghaafiqi mentioned them in Lamahaat al-Anwaar (1127, 1129, 1140, 1141, 1142, 1143, 1144, 1146), except the report of Ibn ‘Umar.
Commentary on the second hadeeth:
It was narrated via two isnaads:
1- From Ibn ‘Abbaas (may Allaah be pleased with him) in a marfoo’ report: “Whoever recites when he prays Fajr three verses from the beginning of Soorat al-An’aam up to the words (interpretation of the meaning): ‘and He knows what you earn (good or bad)’ [al-An’aam 6:3], forty thousand angels will come down to him and the like of their deeds will be written for him. And there will be sent to him an angel from seven heavens with an iron rod, and if the shaytaan instils any evil in his heart he will strike him until there will be seventy veils between him and him. When the Day of Resurrection comes, Allaah will say: ‘I am your Lord and you are My slave, walk in My shade, and drink from al-Kawthar, and wash in al-Salsabeel, and enter Paradise without being brought to account or punished.’”
This was mentioned by al-Suyooti in al-Durr al-Manthoor (3/245-246). He said: al-Salafi narrated it with a unreliable isnaad from Ibn ‘Abbaas as a marfoo’ report, and al-Ghaafiqi mentioned it in Lamahaat al-Anwaar (941).
2- It was narrated that Ibn Mas’ood said: The Messenger of Allaah (peace and blessings of Allaah be upon him) said: “Whoever prays Fajr in congregation and sits in his prayer place, and recites three verses from the beginning of Soorat al-An’aam, Allaah will appoint seventy angels for him who will glorify Allaah and pray for forgiveness for him until the Day of Resurrection.”
This was quoted by al-Suyooti in al-Durr al-Manthoor (3/246) and he attributed it to al-Daylami and al-Ghaafiqi in Lamahaat al-Anwaar (935) in a version close to that of the hadeeth of Ibn ‘Abbaas.
Al-Aloosi said in Rooh al-Ma’aani (7/76), after quoting a number of ahaadeeth and reports about Soorat al-An’aam, including the hadeeth of Ibn ‘Abbaas and Ibn Mas’ood: And there are other reports, but most of that is da’eef (weak) and some of it is mawdoo’ (fabricated), as is obvious. End quote.
There is no proven hadeeth which speaks of the virtues of Soorat al-An’aam.
With regard to Soorat al-Sajdah and al-Mulk, there is no proven report about reading them between Maghrib and ‘Isha’, but there is a proven report about the virtue of reciting Soorat al-Sajdah in Fajr prayer on Friday.
Al-Bukhaari (891) and Muslim (880) narrated that Abu Hurayrah (may Allaah be pleased with him) said: The Prophet (peace and blessings of Allaah be upon him) used to recite in Fajr prayer on Friday: “Alif‑Laam‑Meem. The revelation…” [al-Sajdah 32] and “Has there not been over man a period of time…” [al-Insaan 76] .
And concerning the virtue of Soorat al-Mulk, it is narrated that it may be recited when going to sleep or in general. Al-Tirmidhi (2891), Abu Dawood (1400) and Ibn Maajah (3786) narrated from Abu Hurayrah (may Allaah be pleased with him) that the Prophet (peace and blessings of Allaah be upon him) said: There is a soorah in the Qur’aan, with thirty verses, which will intercede for its companion [the one who recites it] until he is forgiven: “Tabaarak allaadhi bi yadihi’l-mulk (Blessed be He in Whose Hand is the dominion)” [al-Mulk, soorah 67]. Al-Tirmidhi said: This is a hasan hadeeth.
Ibn Hajar said in al-Talkhees (1/234): al-Bukhaari stated that there is a problem with it in al-Tareekh al-Kabeer by noting that it is not known that ‘Abbaas al-Jashami (who is the one who narrated it from Abu Hurayrah) heard it from Abu Hurayrah. End quote.
It was classed as hasan by al-Albaani in some places and as saheeh in others. See: Saheeh Sunan Ibn Maajah, Saheeh Sunan Abi Dawood. Before him al-Mundhiri said: It was narrated by Abu Dawood, by al-Tirmidhi, who classed it as hasan and this version was narrated by him, and by al-Nasaa’i, Ibn Maajah, Ibn Hibbaan in his Saheeh, and by al-Haakim who said its isnaad is saheeh.
Al-Tirmidhi (2892) narrated from Jaabir (may Allaah be pleased with him) that the Prophet (peace and blessings of Allaah be upon him) did not sleep until he had recited “Alif‑Laam‑Meem. The revelation…” [al-Sajdah 32] and “Blessed is He in whose hand is dominion…” [al- Mulk 67] Classed as saheeh by al-Albaani in Saheeh al-Tirmidhi.