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.

What should a woman, who has given several births during different months of Ramadhaan, and didn`t make up for them in addition to forgetting the exact number of the days and years in which she had missed fasting, do ?

She should make up the days of Ramadhaan that she missed after estimating their number, and paying the ransom(in food) due on each day that she had delayed. She should also repay the ransom according to the number of years if she was able to fast before that time, but didn`t.

How long is the` Iddah(waiting period) of a divorced woman?

If a woman is pregnant at the time of divorce, then her 'Iddah (waiting period) expires when she gives birth to the baby. If she is in a state of menstruation, then her `Iddah expires when she finishes three menses. However, if she doesn`t have menses, then her `Iddah expires after three months.

Is the Saum(Fasting) of someone who ate and drank forgetfully while offering fasting of oath expiation invalidated ?

Whosoever eats, or drinks forgetfully is exempted by Allah; therefore, he/she shouldn`t break their fast whether it was obligatory, non-obligatory, or expiatory.