After two years of consecutive non-use, Oyster cards may stop working. You can, in principle, get any money on them refunded at a London Underground ticket office or TFL Travel Centre. I say "in principle" bedcause the policy is that you must produce proof of identification and permanent address, and that any refunds of over £10 will only be made by cheque in pounds sterling to that address. (This is sometimes relaxed but it seems to be at the discretion of the clerk.)
On the other hand, the card may work fine. It's not really clear what the criteria are.
You can only fully register an Oyster card in person at a station. Online, you can protect the card against theft but that does not count as registration.
My mother tried to register her Oyster card at Waterloo with her Irish address a few months back and was told it had to be a UK address. The clerk was being quite obstructive so I don't know whether this is an actual rule or something he made up.
You cannot top up an Oyster card online unless you will be using your Oyster card to make a non-bus journey in the eight-day period starting the day after you top up and can say where that journey will start or end.