Is it permissible for me to name my daughter “Leen”?

“Leen” means “ease”, and there is no harm in giving your daughter that name.

Is it permissible to give Zakah(obligatory charity) to one`s poor sister, or brother?

It is permissible for one to give the Zakah to his poor sister, or brother if providing for them isn`t due on him, and the sister doesn`t receive sufficient provision from whomever that is due on.

Is it permissible for a woman to visit the doctor while in her `Iddah(waiting period)?

It is permissible for her to do that during day time, but it is impermissible for her to go out at night except for a sound reason.

Is it permissible to pay the expiation of an oath to a charitable party as it feeds the poor and needy such as Tkiyet Um Ali?

All perfect praise be to Allah, The Lord of The Worlds, and May His Peace and Blessings be upon our Prophet Muhammad and upon all of his family and companions.

There is no harm on authorizing someone to handle the expiation of another to the poor and needy, since Shafiee's jurists stated that authorizing someone for the purpose of distributing Zakah, expiation and vow is permissible as stated in [Mughni Al-Muhtajj, vol.3 pp.237]. At last, the intention of the person who intends to authorize someone else suffices in this regard. And Allah Knows Best.