If you have an entire itinerary of their daily schedule and are everywhere they are from day to day... that is stalking.
If you follow them home and sit outside their window each night, waiting for them to leave... that's stalking.
If you wait outside a stage door every night, that is obsessive. Nothing more. It's not dangerous. The actor would just think it weird AT MOST. Unless you give an actor a reason to be scared, they won't be. So many people see shows obsessively that performers are used to it.
A cast member told me that there was this one guy that was always at The Full Monty in the front row eating cookies... did the actors always see him? Obviously. Did they think it was strange? Well... clearly. She said he wasn't dangerous or scary... he was just the cookie man.
And, yeah... if an actor gives you their contact info, they expect you to use it. I can understand her hesitance to use it though... I found myself in a similiar situation and you feel like you don't know where the boundaries lie... or worse, you don't want to mistakingly cross them. It's understandable. It's like, 'Well, are we friends now or am I still just a fan to you?... or...? What?' It can get confusing... because, YES, they are just people, but a lot of these people have many fans and in no plausible way could they befriend them all... so you have to question what distance they want to keep you at and understandably so.
"You! You are the worst thing to happen to musical theatre since Andrew Lloyd Webber! And you, well, I just plain don't like you."
~Stewart Gilligan Griffin