Does Imam Ali (a) get included within the Aal-e-Mohammad (pbuh)? If yes, how is it so when he is the cousin of the Prophet (s) rather than his descendant?
The Prophet Muhammad (SAWA) himself declared the names of his Ahlul Bayt who are Aal-e-Mohammad (AS) as Ali, Fatima , Hasan and Husain (AS).
The names of Ahlul Bayt are in many authentic Hadeeths narrated in Shia and Sunni books e.g. Saheeh Muslim , Hadeeth number 4450 narrated from A'ysha that the Prophet covered himself , Ali, Fatima , Hasan and Husain and declared that they are his Ahlul Bayt. It is also mentioned in Musnad Ahmad Ibn Hanbal , Hadeeth number 2903 and in Tirmithi , Hadeeth number 3129, and Sunan al-Kubra by al-Nasaa'ee, Haddeth number 7169, and Sunan al-Kubra by al-Bayhaqi , Hadeeth number 2665 and many other main Sunni books.
Wassalam.