What should a woman, who has given several births during different months of Ramadhaan, and didn`t make up for them in addition to forgetting the exact number of the days and years in which she had missed fasting, do?

She should make up the days of Ramadan that she missed after estimating their number, and paying the ransom (in food) due on each day that she had delayed. She should also repay the ransom according to the number of years if she was able to fast before that time, but didn`t.

Is Zakah (obligatory charity) due on the equipments used in the trading process such as: cars , shops etc..?

No Zakah is due on equipments used in the trading process such as cars and the like.

What is the ruling on a woman driving a car?

All Perfect Praise is to Allah, The Lord of The Worlds, and may His Peace and Blessinsg be upn our Prophet Muhammad and upon all of his family and compnions.

It is permissible for the woman to drive a car, but it is impermissible for her to travel unaccompanied by a Mahram (Unmarriageable kin). And Allah The Exalted Knows Best.

Should one fulfill his vow of donating an animal to the poor and needy with one sheep although he had repeated the vow several times?

Each vow has to be fulfilled, and repeating the words of the same vow for confirmation renders its fulfillment obligatory as one vow. As for multiple vows, they have to be fulfilled as well.