Is It Permissible to Divorce One's Wife for not Praying
All perfect praise be to Allah the Lord of the Worlds. May His peace and blessings be upon Prophet Mohammad and upon all his family and companions.
You should do your best to save her from hellfire by making her observe daily prayers on their prescribed times, even if this means giving her a generous incentive. However, if she insisted on her position, then it is permissible for you to divorce her. And Allah The Almighty Knows Best.
Is it permissible to swear by (Allah "The Living")?
Yes, it is permissible because "The Living" is one of Allah`s Attributes.
Is it permissible to offer Tahajjud prayer after Witr prayer?
It is permissible to offer voluntary prayer after Witr (An odd number prayer performed between Isha and Fajr) prayer. However, it is desirable that the night prayer be ended with Witr. Therefore, it is desirable for one, who thought that he was most probably going to wake up at night in order to offer Tahajjud, to offer Witr after it, but one, who fears that he might not wake up, should offer Witr before going to bed.
My brother is settling a debt on my behalf and in return he takes 30% interest as an additional amount of the whole sum. Is this lawful or not?
This additional amount is considered prohibited interest (Riba) according to Islamic law, and it is not permissible to take it. And Allah Knows Best.