Is food cooked by a non-Muslim halal and can a Muslim eat this food even thou the contents of the cooking are halal?

This depends on whether the person is religious or not. Not every Muslim is devout, just like not every Jew or Christian follows all the dietary or other rules. But let's discuss a person who is a very religious Muslim, and who knows what is expected, according to religious law. Such a person, if they violated the dietary laws and intentionally ate meat that was haram-- in other Words, forbidden because it was not halal, it would certainly be considered a sin; but if the person just made a mistake and is deeply sorry, they should ask Allah for forgiveness and not eat haram meat again.

As for a person who willfully and intentionally violates religious law on a regular basis, that is an especially grave sin. A person who does that shows disrespect for Islam. That person would be in danger of punishment from Allah, which could include hellfire. On the other hand, repentance is the most important thing: if a Muslim sincerely repents and asks Allah for forgiveness, he or she will be forgiven if the offending behavior is stopped.