Is it permissible for one to shake hands with his uncle`s daughter?

No, it isn`t because he is a non-Mahram (Marriageable) to her.

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 .

I`m a building contractor. I have been building a house for a client, but the construction process stopped for some reason. Unfortunately, currently, prices of materials have multiplied, is it allowed for me to demand an increase in the agreed price?

A person prays in a certain spot within the rows of the mosque, and gets angry if someone else prayed at his spot. What is the ruling on this behavior?

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                                                                                                                                                                                                                              Prophet Mohammad (PBUH) make it prohibited for a Muslim from having/taking a certain spot in the mosque when performing prayers if they arrived and find it occupied, furthermore; it is the religious duty on others (praying people) to offer a piece of advice to alert the ones who don't know, that whoever reaches a spot first at the mosque having a priority/privilege upon others in that spot. And Allah Knows Best.