What is the ruling on omitting the prostration of recitation?
Praise be to Allah, and peace and blessings be upon our Master, the Messenger of Allah.
The prostration of recitation (Sajdat al-Tilawah) is a Sunnah for both the reader and the listener. There is no sin in omitting it, though doing so results in missing a great reward. Muslim narrated from Abu Hurairah (may Allah be pleased with him) that the Prophet ﷺ said: 'When the son of Adam recites a verse of prostration and prostrates, Shaytan withdraws weeping, saying: "Woe to him! (and in the narration of Abu Kuraib: "Woe to me!") The son of Adam was commanded to prostrate and he prostrated, so Paradise is his; and I was commanded to prostrate and I refused, so the Fire is mine."'
Sheikh al-Islam Imam al-Nawawi (may Allah have mercy on him) stated: 'It is recommended to prostrate immediately after reciting or hearing a verse of prostration. If one delays it but the interval is short, he may still prostrate. However, if the interval is long, the opportunity is missed.' [Rawdat al-Talibin Vol.1/P.323].
Furthermore, the prostration of recitation becomes obligatory (Wajib) in congregational prayer if the Imam prostrates, out of the necessity of following him. And Allah the Exalted knows best.
Is a woman`s prayer considered invalid if non-Mahrams (marriageable men) saw her offering it?
A woman`s prayer isn`t invalidated if non-Mahrams saw her offering it, but she had better pray in isolation.
A person prays in a certain spot within the rows of the mosque, and gets angry if someone else prayed at his spot. What is the ruling on this behavior?
All Perfect Praise be to Allah The Lord of The Worlds and may His Peace and blessings be upon our Prophet Muhammad and upon all of his family and companions Prophet Mohammad (PBUH) make it prohibited for a Muslim from having/taking a certain spot in the mosque when performing prayers if they arrived and find it occupied, furthermore; it is the religious duty on others (praying people) to offer a piece of advice to alert the ones who don't know, that whoever reaches a spot first at the mosque having a priority/privilege upon others in that spot. And Allah Knows Best.
Is it permissible to pay the Zakah (obligatory charity) for settling the debt of a deceased relative?
It is impermissible to pay the Zakah for settling the debt of the deceased since Zakah is paid to eligible recipients who are alive. As for the debts of the deceased, they are to be settled from the estate before dividing it amongst the heirs, but if the deceased didn`t leave an estate, then it is desirable for his/her heirs to settle those debts if they can afford them. And Allah Knows Best.