If they bust off, save them and try to pin them back on. They are usually far more sturdy when pinned. In fact, I'd probably consider cutting them off any new figures I get and pinning them right from the start.
As far as green stuff, I've had to do that once or twice. Tails aren't too difficult. Similar to the pinning advice, I start by drilling a hole where the old tail was, sticking a bit of wire there and shaping it to the general shape of the tail I want to sculpt, then putting the putty on that. It should be fairly sturdy that way. I usually put rough shaped blog of GS on the wire first, then let that cure. Then put a second layer around that and sculpt the hair texture into that top layer.
Good luck.