1- If she has no contact with her father, she makes her life decisions, and he doesn’t get involved in any of her life decisions, then she doesn’t need his permission. She also doesn’t need her brother’s permission. She can make the decision herself.
2- Does not need to see a Sheikh
3- Yes she can refuse. However, morally she should not upset her mother by disobeying her. If her mother gets hurt, she must avoid that
3- With a Sunni man it can only work it he really believes in the Mut’ah marriage. Sunnis don’t believe in Mut’ah marriage. With a non-Muslim man it is not permissible and not valid
4- Sexual intercourse is haram. But anything else is halal.
5- No she cannot enter a mosque during her period.
6- Yes she can, provided she is confident he won’t pressure her to leave Shia Islam.
7- With a Sunni man it can only work it he really believes in the Mut’ah marriage. Sunnis don’t believe in Mut’ah marriage. With a non-Muslim man it is not permissible and not valid