Most card issuers will insist that you have a UK address that you can use for billing - I have a feeling that it might be part of the 'stop money-laundering' procedures.
It depends. You can live abroad and keep your existing UK bank account, but banks are uneasy about it. It depends on the individual bank and what value you are to them. If you are a fantastic customer they may let you do it, if not, they will ask you to close your accounts. If it doubt, give the bank a correspondence address in the UK.