What is permissible for the person who wants to ask for a woman`s hand in marriage to see from her body?
He is permitted to see her hands and face only, but if he wants to see more, then he has to send a woman that he trusts to do so.
Is it permissible to swear by (Allah "The Living")?
Yes, it is permissible because "The Living" is one of Allah`s Attributes.
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.
Is Fajr (dawn) Sunnah a confirmed one?
All praise be to Allah The Lord of The Worlds Of course, it is a confirmed Sunna which the Prophet (PBUH) used to offer in a regular basis. And Allah Knows Best.