Is it permissible for a woman who broke fasting due to a delivery to pay a ransom?
She should make up for the missed fasting days once she becomes ritually pure, but it is impermissible for her to pay a ransom while being able to fast.
What is the ruling on working for a company that manufactures cigarettes?
All Perfect Praise is due to Allah, The Lord of The Worlds
Working for a company that manufactures cigarettes is forbidden because smoking itself is forbidden, so its production, selling and circulation are forbidden as a result since they aid in committing sin, and whoever aids in that is like the sinner himself. And Allah Knows Best.
I made a vow "If the Israeli troops retreated out of Gaza strip I will buy a cake from a certain bakery" and it happened. Am I obliged to buy from the same bakery?
You are obliged to buy from the same bakery. And Allah Knows Best.
Is it permissible for the guardian, or the father of the child to hit the latter in order to teach him/her good manners?
It is permissible for the guardian to hit his/her child for teaching them good manners once they become ten years old provided that it is done mildly, harmlessly and without intimidation. Actually, such punishment is to be employed gradually i.e. after: asking, warning, and scolding. As for the teacher, he isn`t allowed to hit the student unless the latter`s father approves of it, and it is done according to necessity without intimidation, or harm.