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.
A woman used contraceptive pills, and her menses exceeded (15) days, is it permissible for her to fast?
The maximum of menstrual blood is (15) days, but if it exceeded that due to a medication, or the like, then it is Istihadah (bleeding outside the monthly period), and in this case she should perform Ghusl (ritual bath), pray, and fast. Moreover, she is obliged to make up for the missed fasting days which exceeded her regular menses. And Allah Knows Best.
I work in a government institution that gives an additional three dinars per hour I work. The manager combines students into a single session because attendance is low, and the material taught to all groups is the same. I am paid for two hours, although I actually taught only one session, noting that my transportation costs one and a half dinars. What is the ruling?
The only amount you are permitted to take/have is for one hour work. And Allah Knows Best.