If you're working here, no problem; if you're not, well, you'd get into trouble with your tax-man back home, that's all. I once saw someone wearing a T-shirt that said "I have a secret bank account in the Cayman Islands", but I bet he didn't wear it through US Customs!
Documents: Passport, proof of residence, and local personal references.
Working expats can get mortgages and car loans, as easily as they could back home, I guess.
Plenty of banks.
