Is Zakah due on the orphan`s money?

Yes, Zakah is due on the money of the orphan.

After I had prayed, I found a drop of menstrual blood and was unsure when that happened; what is the ruling on my prayer and fast?

All praise is due to Allah, peace and blessing be upon the Messenger of Allah.

Your prayer and fast are correct ,and you should not make up for them, and we ask Allah, The Almighty, to duely reward you for these acts of worship. Your menses start once you see blood because the situation remains as such unless there is certainty or predominant conjecture, as per the Fiqh maxim: "Certainty is not removed by doubt". And Allah Knows Best.

What should a praying person who doubts having offered one, or two prostrations in the third Rakah (unit of prayer) do?

Whoever has doubts about their prayer should consider what is less i.e. the above person should offer another Sajda (prostration) and complete his/her prayer, then offer Sujood As-Sahw (prostration of forgetfulness). And Allah Knows Best.

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. And Allah Knows Best.