Should I start talking to my friend or no (our beliefs)

It kinds of depends on how important it is to you to have friends who share your faith. For me, it's more important that my friends respect my beliefs (and that I respect theirs) than it is for us to share the same faith. If this friend is otherwise an all-around good friend and person, if you enjoy spending time with her, and if she's not trying to force her beliefs on you (and you're not trying to force your beliefs of her), I see no reason why you should not or can not be friends with her.