For file sharing, you could also investigate the Back To My Mac feature. I've read mixed reports on whether or not this works consistently, but when it does, it sounds like the kind of thing you need.
For remote backup, Time Machine could be tricky - there's an interesting post
here about that. I'd look into the online possibilities, especially if it's not going to be a permanent solution. A quick Google will show you loads of these.
I notice that LogMeIn do one - they are excellent for remote screen sharing, so that might be worth a look. Not sure if it's free though, I'd doubt it.