Is it allowed to shave my beard to join the army taking into consideration that I can`t find a job?
All perfect praise be to Allah, the Lord of the worlds. I testify that there is none worthy of worship except Allah and that Muhammad, sallallahu ‘alayhi wa sallam, is His slave and Messenger.
The army should be joined in preparation for Jihad (Fighting in the cause of Allah), so if Jihad contradicts with growing a beard then it is allowed to shave it. And Allah The Almighty Knows Best.
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 permissible to make up for the missed fasts of the deceased?
A deceased`s missed fasts should be made up for by his/her guardian. It is also permissible to make up for the missed fasts of a deceased relative, and to pay a ransom in expiation for the latter`s missed fasts, which is feeding a needy person for every missed day. However, the guardian`s permission need to be sought by the non-relatives of the dead to fast on his behalf. And Allah Knows Best.
What is the ruling on a man leading his sisters in obligatory prayer, or Taraweeh prayer (Night prayer in Ramadan)?
The prayer of the man who leads his wife, or sisters in prayer is valid, but it is more rewarding for him to offer obligatory prayer in the mosque. And Allah Knows Best.