No.
The United States is not a police state. There are no police road blocks randomly checking people for their papers, that only occurs in Mexico. You are not required to have your papers on you at all times, like it is required of you in Mexico.
Go to Las Vegas (I assume you mean Las Vegas and not Vegas for there is no Vegas), have fun.
He will only have a problem if he gets in trouble and the police get involved. Las Vegas has a lot of international tourists, so not having "papers" is not a big deal. He will, however, need some type of ID if he plans on checking in to a hotel, using a credit card or ordering a drink or tyring to get into a club, if he looks young.
Between LA and Las Vegas there is only an agricultural check point to make sure you are not bringing any plants, fruit or vegetables with you. They do not check IDs there. The only immigration check points are Between LA and the Mexican border. On I5, I15 and state routes 86 and 111.
No - not out on the road. I imagine there's an immigration office somewhere in Las Vegas. Immigration is something you'd only really find at the boarder - like Mexico to California.