Is the prayer of someone who didn`t face Quibla (Ka`ba direction) valid?
All perfect praise be to Allah,The Lord of The Worlds. Facing the Quibla is a condition for the validity of prayer, and the prayer of the person who hadn`t faced the direction of the Quibla is invalid, and he is obliged to repeat it. And Allah Knows Best.
Is permissible to buy/sell with non-Muslim?
Yes buying/selling for a Muslim with non-Muslim is permissible as regards what is lawful.
Is it permissible to offer an absentee funeral prayer?
Yes, it is permissible to offer an absentee funeral prayer.
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.