Sounds like an adventure and a half.
Couple of things that occurred to me:
First, when you bring anything into a country, especially something as big and obvious as a car, customs will tax you on it's value. So you will need to bring paperwork to prove it's yours and that you will be taking back out of the country when you finish your trip. (We have to do this all the time at work with equipment taken out to various countries, but each time brought back to the UK.)
Also, they don't have yearly MOT's like we do, it's something that varies from state to state (from 1yr to 2yrs or not at all). But you will probably need to get your Mk2 tested once it's arrived in the USA.
Have you thought about picking up a banger in New York when you arrive and drive it to SF and sell it there when done? The Top Gear boys did it a while ago. It would certainly save you the hassle of importing and testing, and you might even make a little money for the cause when selling it.
Second, if you're only going for a couple of weeks, you can drive on a UK licence, but you will need an IDP, International Driving Permit for some parts of the USA (again it varies from State to State).
IDP Govt siteThird, you can probably find an insurance company in the USA that will insure an imported car with a driver on a UK licence, but probably only if you have a permanent address. This trip will probably count as something needing specialist insurance. My best bet would be to try calling your current UK insurance company see if they will cover it. If not, call a car insurance broker, they will have a better idea of companies specialising in foreign cover.
Don't forget you'll probably want some sort of breakdown cover, unless you or your co-driver are competant mechanics and will be carrying a complete set of Mk2 spares
You probably won't be able to set up a US bank account unless you go into a branch in person with proof of a US resident address. Some US banks to have an office in the UK, but you'd have to contact them to see if you could set an account up.
Why do you want a US bank account anyway? You can pay with a UK debit card almost anywhere in the USA.
If you want to use dollars, you could try using a top-up debit card, like
FairFX. Its a Mastercard so you can use it anywhere that takes Mastercard, but it's not a credit card. You can get a US $ card and load it up with dollars with your own UK debit card (via website or phone). That way, you are not handing over your own card details every time you pay for something, and the only money going out of that card account will be related to your trip. And it won't go overdrawn either, you can only spend the amount you put on it.
Have you looked at other charity driving things?
One of my old Uni mates has been organising the Dumball Rally for the last few years. Buy a banger drive it across Europe, sell or scrap it and fly home. Take a look:
http://www.dumball.org/Good luck, hope that helps.
