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.
Is it permissible for a person who had vowed to give a certain amount of money to another, but didn`t find the latter to donate that money to the mosque?
In principle, the vowing person should abide by his vow as much as possible. Therefore, if he couldn`t find the person that he had made the vow for, then the vow itself is countless and nothing is due on its maker. However, if the latter happens to find the former later on then, he has to give him that money.
My father passed away, and he had life insurance with "Alico" for an amount of 12,500 dinars. He had paid premiums totaling 2,000 dinars. The insurance company paid us the insured amount. Should we take it, or is it considered forbidden (haram) money? And what should we do with it if it is forbidden?
You may take the amount your father paid to the company. The remaining amount is not yours. However, if you must take it, then accept it and donate it to the poor. And Allah Knows Best.
Is it permissible to trim the eyebrows if they become excessively long?
Trimming eyebrows is permissible if they become excessively long, yet; it is reprehensible. And Allah Knows Best.