You can wash your face with a cleanser (make sure it's gentle and doesn't irritate your skin). I use face wipes that are basically wet wipes but they're small and have cleanser in them or something like that, and they're really gentle on my skin, too. (I have so much acne, and this really helps.) So wash your face every day.
Mood swings. . .Well, I can't tell you when exactly you'll start getting them, but you can always talk to people about how you're feeling!
Periods often start a bit after you start developing breasts, but 'a bit' can be a while. It's also not necessarily a perfect sign. You can't tell when you're going to get your period based on other things in puberty, it depends on the person. (I use a hot washcloth when I get cramps and it really helps.)
