Evidence that "Bismillah al-Rahman al-Rahim" is a complete verse of al-Fatihah

Abdullah bin Abi Mulaykah narrates from the Mother of the Believers Umm Salamah (may Allah be pleased with her) that she mentioned the recitation of the Messenger of Allah (peace and blessings be upon him) (the narrator is unsure whether the word was "she mentioned" or something else). He would recite: "'In the name of Allah, the Most Gracious, the Most Merciful' [Surah al-Fatihah: 1], 'All praise is for Allah, the Lord of the worlds' [Surah al-Fatihah: 2], 'The Most Gracious, the Most Merciful' [Surah al-Fatihah: 3], 'Master of the Day of Judgement' [Surah al-Fatihah: 4]", that is, he would recite each verse separately.

Ibn Abi Mulaykah narrates from Sayyidah Umm Salamah (may Allah be pleased with her) that the recitation of the Prophet (peace and blessings be upon him) was like this: "'In the name of Allah, the Most Gracious, the Most Merciful' [Surah al-Fatihah: 1], 'All praise is for Allah, the Lord of the worlds' [Surah al-Fatihah: 2]", that is, he would recite each verse separately.
Amr bin Harun, who is not strong, also narrated it from Ibn Jurayj and added to it.

It is narrated from Sayyidah Umm Salamah (may Allah be pleased with her) that the Messenger of Allah (peace and blessings be upon him) recited 'In the name of Allah, the Most Gracious, the Most Merciful' [Surah al-Fatihah: 1] in the prayer and counted it as one verse, 'All praise is for Allah, the Lord of the worlds' [Surah al-Fatihah: 2] as two verses, 'The Most Gracious, the Most Merciful' [Surah al-Fatihah: 3] as three verses, 'Master of the Day of Judgement' [Surah al-Fatihah: 4] as four verses, and likewise 'You alone we worship and You alone we ask for help' [Surah al-Fatihah: 5] as the fifth verse, counting them on his five fingers.

Ibn Jurayj (may Allah have mercy on him) said: My respected father informed me that Sa'id bin Jubayr (may Allah have mercy on him) said that 'And We have certainly given you seven of the oft-repeated (verses)' [Surah al-Hijr: 87] refers to Surah al-Fatihah.
(b) Ibn Jurayj (may Allah have mercy on him) narrates from his father: Sa'id bin Jubayr (may Allah have mercy on him) recited to me 'Bismillah al-Rahman al-Rahim' (In the name of Allah, the Most Gracious, the Most Merciful) until he completed the whole of Surah al-Fatihah. Then he said: 'Bismillah al-Rahman al-Rahim' (In the name of Allah, the Most Gracious, the Most Merciful) is the seventh verse (of Surah al-Fatihah).
(c) Sa'id bin Jubayr (may Allah have mercy on him) said to my father: Ibn Abbas (may Allah be pleased with them both) recited this surah to me just as I have recited it to you. Then he said: 'Bismillah al-Rahman al-Rahim' (In the name of Allah, the Most Gracious, the Most Merciful) is the seventh verse (of Surah al-Fatihah).
(d) Ibn Abbas (may Allah be pleased with them both) said: "Allah kept this surah stored for you; He did not send it down to any nation before you."

It is narrated from Sa'id bin Jubayr (may Allah have mercy on him) that Sayyiduna Ibn Abbas (may Allah be pleased with them both) said about the words of Allah 'And We have certainly given you seven of the oft-repeated (verses)' [Surah al-Hijr: 87] that it refers to Surah al-Fatihah. Sayyiduna Ibn Abbas (may Allah be pleased with them both) was asked: Which is the seventh verse? He said: 'Bismillah al-Rahman al-Rahim' (In the name of Allah, the Most Gracious, the Most Merciful).

Al-Suddi narrates from Abd Khayr that Sayyiduna Ali (may Allah be pleased with him) was asked about 'al-Sab' al-Mathani' (the seven oft-repeated verses), and he said: 'All praise is for Allah' [Surah al-Fatihah: 2] (that is, Surah al-Fatihah). It was said to him: The Sab' al-Mathani are seven verses, so which is the seventh? He (may Allah be pleased with him) said: 'In the name of Allah, the Most Gracious, the Most Merciful' [Surah al-Fatihah: 1].

It is narrated from Sayyiduna Abu Hurayrah (may Allah be pleased with him) that the Prophet (peace and blessings be upon him) said: "'All praise is for Allah, the Lord of the worlds' [Surah al-Fatihah: 2] is seven verses, one of which is 'In the name of Allah, the Most Gracious, the Most Merciful' [Surah al-Fatihah: 1]."
And this very surah (al-Fatihah) is called 'al-Sab' al-Mathani' (the seven oft-repeated verses), 'al-Qur'an al-'Azim' (the Mighty Qur'an), 'Umm al-Qur'an' (the Mother of the Qur'an) and 'Fatihat al-Kitab' (the Opening of the Book).

It is narrated from Sayyiduna Abu Hurayrah (may Allah be pleased with him) that the Messenger of Allah (peace and blessings be upon him) said: "When you recite 'Al-hamdu lillah' (All praise is for Allah), then also recite 'Bismillah al-Rahman al-Rahim' (In the name of Allah, the Most Gracious, the Most Merciful). It is Umm al-Qur'an (the Mother of the Qur'an), Umm al-Kitab (the Mother of the Book) and al-Sab' al-Mathani (the seven oft-repeated verses), and 'Bismillah al-Rahman al-Rahim' (In the name of Allah, the Most Gracious, the Most Merciful) is one of its verses."

It is reported from Muhammad bin Ka'b (may Allah have mercy on him) concerning 'seven of the oft-repeated (verses)' [Surah al-Hijr: 87] that it is Umm al-Kitab (al-Fatihah), and it is seven verses including 'In the name of Allah, the Most Gracious, the Most Merciful'.