I want to look at her facebook page
What do you want to look at specifically?
I want to look at her relationships and to get a better sense of who she is
It's bad to stalk people online, even if you think they would like to know you.  Most people post things that are intended only for close friends, and not for strangers to look at.
I won't stalk her, I just want to see whether she's dating anyone.
I guess it's OK if they made the pictures viewable to everyone.