Is it a condition for the mosque where I‘tikaf is performed to hold Jumu‘ah prayers?
No, it is not a condition for the mosque where I‘tikaf is performed to have Jumu‘ah prayers. However, if a person vows to perform continuous I‘tikaf, and Jumu‘ah occurs within that period, then they must observe I‘tikaf in a mosque where Jumu‘ah is held so that they do not break their continuity by leaving for Friday prayer.
When is the prayer considered *adāʾ* (performed within its time): upon rising from the bowing (*rukūʿ*), or after rising from the prostration (*sujūd*)?
All praise is due to Allah, and peace and blessings be upon our master, the Messenger of Allah.
Whoever catches one complete rakʿah within the prayer's time has caught the prayer as an on-time (adāʾ) prayer. The rakʿah is complete when the worshipper raises his head from the second prostration (sajdah), even if he has not yet reached the degree of standing in which the recitation is valid.
It is stated in Nihāyat al-Muḥtāj (Vol.1/p.378): "What is meant by the rakʿah is the completion of all of it, with its two prostrations." End quote.
And in Ḥāshiyat al-Shabrāmallisī: "(His saying: 'a rakʿah') means that he raises his head from the second prostration, even if he has not reached the degree in which the recitation is valid." And Allah Almighty knows best.
________________________________________
Note on terminology: Adāʾ refers to performing the prayer within its prescribed time, as opposed to qaḍāʾ (making it up after its time has ended).
The imam recited a verse containing a prostration of recitation (*sajdat al-tilāwah*) but did not prostrate. After the imam's *salām*, a follower (*maʾmūm*) performed a prostration of forgetfulness (*sujūd al-sahw*) because the imam had not performed the prostration of recitation. Is it permissible to go against the imam in this way?
All praise is due to Allah, and peace and blessings be upon our master, the Messenger of Allah.
There is no sin on the imam if he omits the prostration of recitation (sujūd al-tilāwah), even deliberately. The maʾmūm (the one following the imam) is obliged to follow the imam in the prayer, so if the imam does not perform the prostration of recitation, it is not permissible for the follower to prostrate, because the imam is appointed only to be followed.
If the follower introduces a prostration after the imam’s salām but before his own salām, in a case where there is no prostration of forgetfulness (sujūd al-sahw), his prayer is invalidated if he knew it to be prohibited. Otherwise, he is excused on account of his ignorance and his prayer is not invalidated.
It is stated in Ḥāshiyat al-Imām al-Jamal ʿalā Fatḥ al-Wahhāb: “His statement: ‘So the omission of the hayʾāt (the non-essential sunnahs of the prayer) is not compensated for by prostration; if one prostrates for any of them deliberately, his prayer is invalidated, unless he is excused due to his ignorance.’”
Since this issue is one that is hidden from the laymen, as it is among the subtleties of knowledge, and the laymen are excused for ignorance of whatever is of such a nature, and their act of obedience is not invalidated because of it, it may be said that the prayer of one who has not acquired knowledge of this issue is not invalidated, with the necessity of learning the rulings remaining. As for after knowing it, the prayer is invalidated. And Allah Almighty knows best.
Is it permissible for a praying person to make supplication in each Sajdah (a prostration) of obligatory prayer?
It is permissible for a praying person, whether praying individually, or in congregation, to make supplication during Sujood (prostration) in obligatory, or voluntary prayers. However, it is disliked for the Imam to do so since he is required to spare the prayer performers any sort of hardship, unless he is leading a certain group who don`t mind him extending the prayer.