In reply to ClimberGirl:
As has been said, you're right not to jump on a climb with any random and expect a good belay, but at the same time, being too sceptical will hinder your progress.
Maybe find two others to climb with, and as you rotate round, watch the other two, see if you're happy with how they belay.
Fall practice! Deliberately jumping off not only tests your belayer, but will boost your confidence. Sometimes I'll throw myself off an easy route, before I work something hard, just to get the fear out of me!
The biggest fall you'll ever take is going to clip, missing, and falling. So bare that in mind when practicing, there's no need to practice mega whippers as an indoor climber.
Rope burn might've come from holding something near to a QuickDraw as you fell? I wouldn't worry about it.
Leg behind the rope is a pain, I'm regularly guilty of it. On easy routes, I let it happen cos I know I'm probably not falling, and on hard routes, I'm too focused on the route to care. Took a nasty whipper complete with inversion last week, and got a pointy volume to the back. But, other than a bruise, I was fine, so i didn't let it bother me. I know I need to sort it though, cos it could've been worse. A good belayer should shout it out to be fair.
I don't wish I'd known anything when I was younger or starting, I think you need to learn these things as you go, and get stronger and improve. Maybe have a look at Dave macs book 9 out of ten climbers.
Don't focus on grades, just see if it looks good, and get on it. For some reason, I have a thing where I hate climbing 6c. I'm comfy at 6b+, and I love working 7a, but 6c just puts me off. No idea why. But I'm starting to ignore that more now, and just going for it, as I'm learning that grades can vary so much!
Anyhow, you're young, and have plenty of time, don't put too much pressure on yourself.