Buffy has...issues with our dad. Not my place to get into the nitty gritty of it, but let's say that it's complicated. The fact that our dad kept you a secret from us and kept you away from us, well, it probably just brings them all out even more. Not your fault, obviously.
No, you didn't have a Watcher training you, but you have at least physical training. The Watcher training is super important, too, but it sounds like you've had the physical stuff decently covered.
Wow, I can go out drinking with my little sister.
Actually, how much do you know about the other parts of Slayer-ing? Like, the history, the different types of demons you could face, that sort of thing?