My best friend is getting on my nerves (facebook, texting etc.)?

If you want to keep this friend, then you need to sit her down and talk to her. Tell her how you feel about the being late thing and that it frustrates you. The next time she gets mad about something stupid, then confront her about it. Ask her why she's mad and that you were doing something. She probably feels like she is losing you and your other friend, so she is feeling bad about herself. Also, tell her that it seems rude to other people that she puts things like "wish i was invited". If she means a lot to you, then just try to sit her down and talk to her about it all. Otherwise, get a new friend.