This girl is insecure and has anxiety issues. That's driving a lot of her behavior.
I'd never take her serious. This one is acting too poorly, too early in the game. That never ends well.
She also seems to be very avoidant, thus after they meet and hang out she starts thinking about things and pulls away. If that is the case, it could be a constistently frustrating issue.
I think OP should just mimic her behavior. If she backs away, he backs away. Have fun when they get together and not worry so much about her behavior when they arent together. Let her wonder about him instead of the other way around. That in itself will build attraction and value on his end. If all goes well, she will stop overthinking it and want to see him more, which will eliminate the pull backs.
Age is only a thing if the man makes a big deal out of it. Dont act like its a big deal and it wont be a big deal.
Being this early on, just make the next date, see her there. No need for constant messaging and talking non stop in between dates/hanging out. That will keep her wondering and also build attraction/value.
Just my opinon.