Is it permissible for the young woman to turn the suitor down if she had no feelings for him?
Yes, it is permissible for her to do so.
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.
What is the ruling of Islamic Law on a person who abandons prayer after reaching puberty—is he required to make them up?
All praise is due to Allah, and peace and blessings be upon our master, the Messenger of Allah.
Making up missed obligatory prayers is an Islamic duty just as performing them in their proper time is obligatory, and taking care of them takes precedence over performing voluntary prayers. This is established by the practice of our Supreme Prophet (peace and blessings be upon him) when the polytheists distracted him on the Day of the Trench from performing the Asr prayer, so he made it up afterward, as well as the Hadith: "Pay Allah what is due to Him, for Allah is most deserving of fulfillment." (Recorded by Al-Bukhari)
Furthermore, it is valid to make up missed prayers at any time.
Whoever has missed a number of prayers and does not know their exact count, it is obligatory upon them to sincerely repent and exert their utmost effort to estimate their number. If they are unable to determine the exact count, they should base it on what is most probable according to their best judgment. They should then make them up gradually; if one performs one missed prayer alongside every current obligatory prayer, the matter becomes easy and manageable, and with the passage of time, one will complete what is owed, Allah willing. And Allah Almighty knows best.
Is it permissible to offer condolences to a non-Muslim?
All praise is due to Allah, and peace and blessings be upon our master, the Messenger of Allah.
It is permissible to offer condolences (Ta'ziyah) to a non-Muslim upon the death of their relatives. This constitutes a form of benevolent treatment (Birr) that we have been commanded to observe. Allah Almighty states {what means}: "Allah does not forbid you from those who do not fight you because of religion and do not expel you from your homes—from being righteous toward them and acting justly toward them. Indeed, Allah loves those who act justly." (Surah Al-Mumtahinah, 60:8). And Allah Almighty knows best.