1. Yes.
2. No. The pre-75 and pre-78 125s race (and are scored) together.
3. You apply for your number when you join the club. If you ask for a number that's already taken, then you get to chose again. Worst case scenario is that you turn up with some white electrical tape and some scissors... This bit always stresses people out, but really, its rarely a problem... And its easily sorted if it happens. Check out some photos from HEAVEN events to get an idea of the numbers already in use.
4. It would have until you told everyone that it's Nev's old bike!
Seriously, the main things that people get knocked back on:
Throttle not self returning (this is a Nev favourite);
Handle bar ends not plugged;
Wobbly wheel bearings and/or swing arm bushes;
Loose spokes;
No balls on the end of levers.
Really, if the bike is in the sort of condition that you'd be happy to race it, chances are that it will be fine.
At the club level, they're pretty easy going WRT eligibility - particularly as a newbie, I'd be more than amazed to see you cop a hard time over an eligibility issue.