Is a woman`s prayer considered invalid if non-Mahrams (marriageable men) saw her offering it?
A woman`s prayer isn`t invalidated if non-Mahrams saw her offering it, but she had better pray in isolation.
Can the Christian widow whose married from a Muslim become an heir of his?
All perfect 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.
A Christian widow can`t inherit her Muslim husband because their religions are different. 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.
If husband doesn`t pray, but wife does, is their marriage contract considered valid or not?
All perfect praise be to Allah the Lord of the Worlds. May Allah`s peace and blessings be upon our Prophet Mohammad and upon all his family and companions.
Not observing daily prayers is a grave sin, but doesn`t invalidate a person`s marriage contract. However, we advise you to save your husband from hellfire by convincing him to observe the prescribed prayers. And Allah The Almighty Knows Best.