1- The first part of the verse is talking about the wives, since it uses the feminine plural pronoun. But then in the middle of the verse it switches to the masculine plural pronoun كم so we know that the subject changed. It seems that the Qur’an is indicating to us: don’t think that the wives of the Prophet (s) are infallible. Only these members of the Ahlulbayt (a) are infallible.
2- Yes this verse is part of the same verse that talks about the wives. But the pronoun changes from كن to كم which means the subject changed.
3- As for the app, it means the beginning of the verse is addressing the wives of the Prophet (s). It’s not referring to the second part of the verse. Break the verse into two clauses. The first is about the wives (and by extension it includes all women), and the second is about the 5.
4- The flow of the verse indicates that the subject changed due to the pronoun changing. If the pronoun hadn’t changed then yes the verse would be addressing the wives. But when the pronoun changes, the subject changes, so now we know those being addressed changed, so we have to investigate who the new subject is. When we examine sahih hadiths, the hadith tells us the new subject is those 5 peace be upon them.
5) Yes I am referring to Sunni and Shia hadith. Sunnis have narrated in their sahih works that only the 5 were under the cloak, and the Prophet’s (s) wives, such as Um Salama (who was a righteous lady), were not allowed to enter.
See the following:
One day the Prophet (S) came out afternoon wearing a black cloak (upper garment or gown; long coat), then al-Hasan Ibn ‘Ali came and the Prophet accommodated him under the cloak, then al-Husayn came and entered the cloak, then Fatimah came and the Prophet entered her under the cloak, then ‘Ali came and the Prophet entered him to the cloak as well. Then the Prophet recited: "Verily Allah intends to keep off from you every kind of uncleanness O’ People of the House (Ahlul-Bayt), and purify you a perfect purification (the last sentence of Verse 33:33)."
• Sahih Muslim, Chapter of virtues of companions, section of the virtues of the Ahlul-Bayt of the Prophet (S), 1980 Edition Pub. in Saudi Arabia, Arabic version, v4, p1883, Tradition #61.
Sahih al-Tirmidhi narrates on the authority of Umar Ibn Abi Salama, the son of Umm Salama (another wife of Prophet), which is as follows:
"Verily Allah intends to … (33:33)"
was revealed to the Prophet (S) in the house of Umm Salama. Upon that, the Prophet gathered Fatimah, al-Hasan, and al-Husayn, and covered them with a cloak, and he also covered ‘Ali who was behind him. Then the Prophet said: "O’ Allah! These are the Members of my House (Ahlul-Bayt). Keep them away from every impurity and purify them with a perfect purification.”Umm Salama (the wife of Prophet) asked: "Am I also included among them O Apostle of Allah?”the Prophet replied: "You remain in your position and you are toward a good ending."
Sunni reference: Sahih al-Tirmidhi, v5, pp 351,663