That would be very cool to print a new car, but realistically it's cheaper to buy one if you consider the cost of your time and materials. I mean you have to render all the parts and assemble the thing. Then there's parts like wiring harnesses you still have to make by hand. Still how awesome would that be drive a car you made yourself.

As far as I know, generally you can register a home built car in the USA, but it varies by state. Different states have different regulations. Typically you just have to jump through some inspection hoops. Not too long ago I converted a couple off-road motorcycles to street legal in Nevada and it wasn't difficult. Though in states like New York and California a gas powered car may have additional smog regs impossible to get past. A lot easier for an electric one, no smog regs.

As far as the copying, you would only be infringing on any patents or trademarks that may exist. Those are regional and I don't believe they apply to personal use. Even if they did, I doubt any car maker is going after someone who makes a personal copy of their car. Now if you tried to produce and sell copies, that could get you a lot of attention. But even then it depends where you're doing it. In China they mass produce exact copies of popular western cars even down to the trademarks, but they don't export them and China doesn't care so there's nothing to stop them.