Is it permissible to swear by (Allah "The Living")?
Yes, it is permissible because "The Living" is one of Allah`s Attributes.
What is the Islamic ruling regarding a person finding buried treasure, whether gold or artifacts, and what is their share of it?
If the buried treasure is Islamic, it is considered Luqta (lost property), and the finder must announce it to locate its owner. If all efforts to find the owner fail, the finder may take ownership of it. If the treasure is non-Islamic and consists of gold or silver, zakat must be paid on it, which is one-fifth of its value. And Allah Knows Best.
Is it permissible to repeat the Istikhara (seeking guidance) prayer, and is it a condition that one should sleep after offering it?
All perfect praise be to Allah,The Lord of The Worlds Istikhara is offered once, but it is permissible to repeat it, and sleeping after offering it is not a condition for its validity. And Allah Knows Best.
How many pieces of cloth are used to enshroud a deceased man, and a deceased woman?
A deceased woman is enshrouded in five pieces of cloth: head cover, wrapper, shirt , and two folds of cloth. On the other hand, a deceased man is enshrouded with three pieces of cloth.