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.
You can buy a car for that much money.
Yes
no
yes
No, you cannot work in the US with a tourist visa.
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.
car lot