I have friend living in CA. If my friend have USA pastport. He can live in TJ and go to work at US everyday? That means can he cross over the border everyday to go to work at USA??

Yes. The US will not give him problems but Mexico requires a dual citizenship if they know he lives in TJ. Tons of people do it anyway without ever getting a dual citizenship but there are some Mexican officials that will hassle people if they know you live in Mexico. I think they give you 6 months free or something like that and then they want you to pay for a permit for a longer time period or get a dual citizenship. It's just that they want money basically but he can probably het away with it anyway since he has a passport. Mexico officials are actually deporting Americans back to the US if they don't have a passport to get into Mexico now. There are some tricks around it but there are some Mexican border supervisors that are strict and may give him a hard time.

Yes indeed. There are many doing just that.