1. A friend to call my own means a friend. we often use the phrase (a something) to call my own, which means something that you own, it often suggests that you don't own many things.
It is often used in the negative: He doesn't have a house to call his own.
2. Yes, it means that I'm your true friend, and it is is fairly common usage. Your other versions of the phrase could be used, but we don't here them much at all, especially I've got a friend in you, which I have never heard being said.