Lol. You should be equal. Guys talk down to you because they can. Their macho guy friends think that is how they are supposed to act and talk. You need to correct them on this. Not me. Tell them that the next time he calls you babe, you are going to kick him in the bal!s. And then do it. Same with chick. Just say no.
I suspect that you are stuck with custard girl for a while.
You cannot change the world, but there is no reason to let your guy friends be Neanderthals. Your women friends can call you whatever you let them. Women frequently call each other girl. Lesbians and gay guys can call each other queer, but the nonfriends should not.
Be strong. Be assertive. You can control this.