I don't think my friend is a bully or mean. But my friend pushes me, punches me in the arm sometimes, and wrote "I am a dork" on my hand. Should I be friends with her?

Do you like it when she does those things? Have you told her to stop? If so, what is her response?

I get the impression that you know this is not the way friends treat each other. Why don't you try saying something to her. If she listens to you, and makes some changes, then remain her friend... maybe it is just her way of joking around. But, if she ignores your requests, or treats you badly because of it, she doesn't sound like much of a friend.

Think of it this way: If your best friend or sister told you about a friend of theirs who was treating them like that, what would you tell them?

Guys often joke around that way (well, us immature ones do anyway) but as Doula said, if it makes you uncomfortable then you should tell her that and ask her to stop. If she doesn't stop, there is your answer.