Am I permitted to perform more than a prayer within single ablution?

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.

You are permitted to pray as many as you could within one ablution and to recite Quran so long as your ablution isn't nullified. And Allah Knows Best.

Is it permissible to make up for the missed fasts of the deceased?

A deceased`s missed fasts should be made up for by his/her guardian. It is also permissible to make up for the missed fasts of a deceased relative, and to pay a ransom in expiation for the latter`s missed fasts, which is feeding a needy person for every missed day. However, the guardian`s permission need to be sought by the non-relatives of the dead to fast on his behalf. And Allah Knows Best.

Is it a condition that the meat of the Eid sacrifice should be distributed in order for the sacrifice to be accepted by Allah?

The poor and needy should be given from that sacrifice , even if it be a small portion,(One kilo for example) as raw meat so that they would cook it the way they want. The remainder of that sacrifice is either distributed, eaten, or offered to people in a banquette .

Is Zakah (obligatory charity) due on the Zakah money received by a poor person, and reached a Nissab (minimum amount liable for Zakah), and a whole lunar year had lapsed over having it in his possession?

Yes, the poor who possessed a Nissab for a whole lunar year is obliged to pay the Zakah due on that money even if it was given to him as a Zakah money in the first place. And Allah Knows Best.