1. Your bike might be safe. There's plenty of places to chain it up, and I never saw a bike that had been vandalised or anything, but my housemate did have hers stolen (when it was chained up).
2. Yes, lots. But there's also a lot of cyclists, so finding somewhere to put it might be a problem. There seems to be quite a few people chaining theirs to fences outside teaching buildings.
3. Park villages aren't covered, some of the park houses (but not all), and brighthelm's are. I don't think east slopes are either, but you might have better luck with the newer, nicer halls. You aren't really meant to bring your bike inside, but in park village, brighthelm and maybe east slope it would usually be ok so long as it's not on your cleaning day, or if you keep it in your room.