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.
What is the ruling on making up for missed fasting after the second half of Sha`ban (the month before Ramadhaan)?
One is obliged to make up for missed fasting before the start of next Ramadhaan, and regardless of offering it during the first, or the second half of Shab`an. This is because the prohibition mentioned in the Hadith is for offering absolute voluntary fasting in the second half of Sha`ban. And Allah Knows Best.
Should missed Sunnah prayer be made up?
Making up missed voluntary acts of worship is from Sunnah.
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.