>>6 Don't force your friends to get along. Just because you're friends with them doesn't mean they have to be friends with each other, and it's rude to act like they should. Tell Anna that you're staying friends with both of them but that you respect she's not a fan of Jane. Tell Jane that you have more than one friend and can't give her all of your time. If they don't like it, they can hang out with someone else.
It's also good policy to stick with the plans you make first. If Anna asks you to hang out with her and do a project one night and you agree, and then Jane asks you to go to the movies, her treat, on that same day, don't ditch Anna. Whoever you make plans with first is the one you stick with no matter how much more interesting the second offer is.
Good luck :o