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?
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.
What should a woman who delayed making up for missed fast, due to menstruation, till the start of the next Ramadan?
Whosoever broke fasting in Ramadan, and was able to make up for it, but didn`t until the next Ramadan started, is obliged to make up for the missed days, and to pay the ransom as well. However, if he/she wasn`t able to before next Ramadhaan due to an excuse, then he/she should only make up for the missed days. And Allah Knows Best.
What is the ruling on someone who perform their prayer after finishing it because they believe they missed a Rak'a, a prostration, or that they did not perform it correctly (thinking their prayer was invalid)?
If he was sure that his prayer is void then reperforming it is an obligation along with figuring out the reason of invalidity so long as this wasn't out of uncertainty. And Allah Knows Best.
Is it permissible for a Muslim woman to marry a Christian man?
All perfect praise be to Allah the Lord of the Worlds. May His peace and blessings be upon our Prophet Mohammad and upon all his family and companions.
It isn`t permissible for a Muslim woman to marry a Christian and such marriage, from an Islamic position, is invalid. And Allah The Almighty Knows Best.