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.
What is the ruling on one who feels drops of urine falling during ablution?
If he is certain that urine is exiting from him during ablution, then his ablution is invalidated. He must remove the impurity from his clothes and body and repeat the ablution.
However, if what he feels regarding urine exiting is merely doubt or illusion, then ablution is not invalidated by doubt and illusion. He should not pay attention to it, and it is not permissible for him to follow the doubt and whispers that corrupt his religion. And Allah the almighty knows best.
What is the ruling on wiping the white area behind the ears instead of wiping the head?
The obligation in ablution is to wipe some of the head; it is not a condition to wipe all of it. Wiping the white area behind the ears suffices for that. And Allah the almighty knows best.
What is the ruling on eating or drinking forgetfully during the day in Ramadan or during voluntary fasting?
Whoever eats or drinks forgetfully while fasting, whether in an obligatory or voluntary fast, should continue their fast, for it is Allah who has provided them with food and drink. There is no difference between obligatory and voluntary fasting in this ruling.