You need to give specific information. As I guess it is same at your home country, some laws are enforced strictly and some laws are loosely enforced in the U.S.
As for stopped by police, if you were stopped by a police then you simply follow what the police say. You may have heard on the news about police officers in the U.S. especially against minorities. However, it is TV news, most of the time if you have done nothing wrong then there is nothing to worry about if you have stopped by police in the U.S.
As far as if you can kill a person if a thief got into your home. Such law is called Castle Doctrine or non-lawyer people like us may know more as “Make My Day Law.” And yes, Nevada (the state Las Vegas is located) has Castle Doctrine. However, each law is written differently and has to understand how Nevada Castle Doctrine is written to understand how this law works. It is not as simple as you can just kill a person.
I do find little interesting that you are asking such questions on a website like FlyerTalk. Also, out of all the places in the U.S. why are you interested in moving to Las Vegas?