Is the marriage contract considered valid if concluded at home by the marriage official (Ma`zon)?
Yes, it is valid as long as it is registered at the court.
Some people eat raw lamb live. Is this permissible or not?
Praise be to Allah the Lord of the Worlds. May His peace and blessings be upon our Prophet Mohammad and upon all his family and companions.
There is no harm in eating raw lamb liver since this is permissible according to Sharia. And Allah The Almighty 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.
Are phone conversations between the two sexes permissible if for consultation, and within the limits of good manners?
Such act is impermissible since it renders hearts corrupt, and could lead to forbidden attachment. Allah, The Almighty, Says (What means): "and follow not the footsteps of the devil." [Al-Baqarah/68].