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.
Is it a condition for I‘tikaf to be performed in the mosque?
Yes, for I‘tikaf to be valid, it must be performed in a mosque. I‘tikaf is not valid if performed at home or elsewhere.
What is the ruling of Islamic Law on performing the Witr prayer after the Adhan for Fajr prayer?
All praise is due to Allah, and peace and blessings be upon our master, the Messenger of Allah ﷺ.
The time for Witr prayer begins after the ‘Ishā' prayer and ends with the rising of true dawn (al-fajr aṣ-ṣādiq). If a Muslim performs it at any point within this window, it counts as performed on time.
It is also recommended to make up a missed Witr prayer at any time — whether before or after performing the Fajr prayer, or at any other time of day. On the authority of Abū Sa‘īd al-Khudrī (raḍiyallāhu ‘anh), the Messenger of Allah ﷺ said: "Whoever falls asleep and misses the Witr prayer, or forgets it, let him pray it when he remembers, or when he wakes up." (Related by at-Tirmidhī)
Shaykh al-Islām, Imam Ibn Ḥajar al-Haytamī (raḥimahullāh), says: "The time for Witr prayer is between the ‘Ishā' prayer and the rising of dawn, based on the authentic ḥadīth to this effect. If this time has passed, it is permissible for him to make it up (qaḍā') afterward." [Tuḥfat al-Muḥtāj]. And Allah, the Exalted, knows best.
Is it permissible for a mother to stop her daughter from marrying a respectable, God-fearing young man because he isn't college/university graduate?
It is impermissible to deny a woman her right in getting married except for a lawful reason, and problems can be solved through dialogue. However, she can file a suit in order for the judge to have a say in that regard.