If it's a new car, you'll need a valid US address and/or driving license.
Yes
Yes, a foreigner can buy a car in Mexico. They will need to provide the necessary documentation, such as a valid passport, visa, and proof of address, and may also need to obtain a temporary import permit for the vehicle.
I don't know about buying life, but you don't have to be a citizen to buy property.
Yes. A person does not have to provide proof of citizenship to purchase real property in the US.
no
yes
see you in jail!
Yes, a foreigner in a new country can buy, sell, or trade personal possessions. If the foreigner came to a country with possessions, the person keeps them-- unless it would damage the country's ecosystem.
You can buy a car for that much money.
no
No, you have to be a US Citizen.
Yes, a foreigner can stay in the US if they marry a US citizen by applying for a marriage-based green card, which grants them legal permanent residency in the country.