Is it permissible to listen to chants praising the Prophet if accompanied by musical instruments?
If singing, or chanting in praise of the Prophet was accompanied by a forbidden musical instrument, then it is forbidden.
Is the father a Mahram (Non-marriageable) to his son`s mother-in-law?
The father is a non-Mahram (Marriageable) to his son`s mother-in-law, so it is impermissible for them to look at each other, or to have a seclusion (Khalwah).
Is it permissible for a person to give the Zakah (obligatory charity) to his daughter-in-law?
Yes, it is permissible for a person to give the Zakah to his daughter-in-law if she was poor, and none provided for particularly by whom are obliged to provide for her. And Allah Knows Best.
My eyebrows are very thick. Is it allowed to reduce them by cutting?
All perfect praise be to Allah the Lord of the Worlds. May His peace and blessings be upon our Prophet Mohammad and upon all his family and companions.
It is allowed to reduce thick eyebrows by cutting them, however, it isn`t allowed to pluck or make very thin. And Allah The Almighty Knows Best.