Didn't look hard did you - try the "want to get into racing" and "competitions/races" threads in this very forum...

No, you don't need to be part of a club, but if you want national ranking points you need a licence, available from British Cycling.
It's much preferred by the organisers (and those of us who hate queueing for uplift) if you enter races at least a week (ideally two) in advance, so that the organiser knows how many people to organise transport/toilets/etc for.
15, you'll be in Youth category, unless you want to run in the Hardtail cat at any race that provides one (not all do).