Assuming your IP is private when you connect to any p2p network is foolish. They all work the same way, by providing direct connections between clients. So anyone you download from is going to have your IP address.

BitTorrent, unlike other P2P services has no central server making it far safer. There is nothing to login to and nothing to signup for, therefore no central "log" that can be subpoenaed. The individual BitTorrent clients create a network between themselves and each downloader takes responsibility for the file's delivery. It's pretty genius actually.

If your downloads are never starting it means there aren't any seeders (uploaders) for that file or they can't reach your computer because you're behind a router or some kind of internet connection sharing. In the latter case you just have to forward the appropriate ports to the computer you're running BT on.

People logging into old-school Napster-like services are one subpoena away from a MPAA lawsuit It's happened so many times already.