The best way to sex it is by probing near the anus (sniggers). I’ve not done and will probably ask a mate to do it. You can look at the spurs (again near the “ahem”) but that can be harder to accurate. Though I suspect mine is a male. 😀
Pigface, it depends on what type of spider it is. Is you have any photos I could let you know. It probably could live a few months without food. The main problem would be what it drinks. If your house is humid enough it should be ok. Failing that, if it does catch some prey it would eat and drink that. If it’s bum is looking small and your house it quite dry you could lightly mist its web, maybe once a week. Over all spiders are pretty good at looking after themselves.