China is great for visitors, especially lighter skinned visitors. You probably won’t go to jail in China unless you have a thing for drinking a lot in Chinese bars, even then you will probably be ok as long as you don’t pick any fights.

Illegal immigration really isn’t a thing in China beyond a few North Koreans in Dongbei and a few Laotians in Yunnan. So they just won’t assume you are an illegal immigrant.

You should also know that China doesn't have as much rule of law as America and indeed average people have a lot to worry about around the police, and generally are very careful not to do things that will get them beaten up. But it happens nontheless - violent assaults on street sellers by police, for instance. In China, people are actually scared of the police because the policemen have so much arbitrary power. They're not strictly and fairly enforcing the law at all.