Are there laws to put real car models in a game?

Your first point makes no sense in a modeling environment.
There is absolutely no way that you could ever create an exact 1 to 1 replica that infringines on any copyright by not having at least 7 different features from reality somewhere - short of doing something stupid like actually 3d scanning the car.

Their case would likely never hold up in court - especially if like you mention at the end you purpously change some features.

The way I remeber it. You only need 7 different design points. And within a car, thats easily achievable depending on the degree of the copyright the company has in place.

Again - not telling anyone that they should “just do it”, it is easier to contact the company and get a yes/no.