What is the Islamic ruling on one who was unable to fast and then regained the ability?
He is not required to make up the fast (Qada) even if he becomes capable of it; whether he regained the ability to fast after paying the fidya (feeding a needy person for each day of missed fasting) or before it, because he was liable for paying it in the first place, so it remains binding upon him. However, if he delayed paying it beyond the first year, nothing is required of him due to the delay. If he is unable to pay it, it does not remain as a debt upon him. And Allah the Exalted knows best.
Is it permissible for a woman to shake hands with her brother-in-law?
It is forbidden for the woman to shake hands with her brother-in-law because he isn`t a Mahram (unmarriageable) of hers.
How is night prayer offered?
Night prayer is offering voluntary prayer after Maghrib and before Fajr (Dawn). As for Tahajjud, it is offering voluntary prayer at night after waking up voluntarily, and for Allah`s sake as He Says (What means): "And pray in the small watches of the morning: (it would be) an additional prayer (or spiritual profit) for thee: soon will thy Lord raise thee to a Station of Praise and Glory!" [Al-Isra`/79]. Offering Tahajjud is better than offering voluntary prayer before going to bed.
Is the marriage contract considered valid if concluded at home by the marriage official (Ma`zon)?
Yes, it is valid as long as it is registered at the court.