Yes, as long as you have the cash.
Buying isn't the problem, with enough money, it is the legal operation of the vehicle, and securing a valid driver's license.
no
Yes
You can buy a car for that much money.
yes
I had a Norwegian buddy in college who owned a Honda, and every illegal immigrant can buy a car. Cars aren't restricted to US nationals.
If it's a new car, you'll need a valid US address and/or driving license.
They are often less expensive.
In the car crushing yard
If you're too ashamed to tell us what the car is, the answer would probably be no.
Yes
Wouldn't be a simple thing to do. The problem is that the car would have to be registered, and the person registering it would have to hold a drivers license in the state they're registering it in, and, in order to be eligible to get a drivers license here, they'd have to establish themselves as a resident of that state (in which case, they'd have to become a resident of the US, at which point, they cease to be a tourist).