1. Not sure. I'm not even sure if Buddy Spy even works correctly anymore at all.
2. Yes, it's safe. It needs to log in because you're only able to scan the statuses of people on your buddy list only (at least through the way BS uses).
3. Offline means invisible and online means available.
4. I guess the web checkers. Buddy Spy hasn't been updated in a while as far as I know.