You need a UK address to register the car, tax the car and usually to insure the car as well. I’m not sure how/if a US insurance policy would work in the UK.
Do you have any friends or family in the UK who might be able to lend you a car while you are visiting, rather than you actually buying one?
There are no age restrictions as far as I know.
There’s no such thing as a visa waiver program for the UK though - that’s a US program only. Instead you will be ‘applying’ for a visa at the border each time you enter the UK. They don’t have to let you in for 6 months... if they think you might be an overstay risk, they may just let you in for a couple of months, couple of weeks or even a couple of days.
If UK immigration believe you are spending too much time in the UK or are attempting to use the visitor visa to live in the UK, or don’t have enough ties to the US to prove you will return (a job, home, family, commitments etc.) they may refuse you entry to the UK.
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