Some girls don't know what they want, this person sounds like she's not really sure of what she wants but definitely having you in the mix and knowing that you like her so much is boosting her self-esteem sky high and she would probably never want to see you move on.
If she's making time for other guys who are literally just as far away from her as you are, then she's taking the piss.
Did a long distance relationship for 4 years, we were in separate continents. Marriage was on the cards at one point, then I found out he'd slept around with other people for 3 years. Not all long distance relationships are doomed to fail but you haven't even made it past the 1 year make it/break it mark... And already she's into other people.
From what you've described, you're not communicating enough, discussing explicitly how you feel, I mean, she wants you to be jealous, most girls will happily want you to be jealous, makes em' feel protected and loved and they feel like they're hot sh*t.
In all honesty, you could do better. Here you are investing all your energy into this, and look, you're even resorting to Student Room for advice. Do you think she has?
Ultimately, its up to you, to me she sounds like she's messing you around a bit, if I were in your shoes (and I'm only saying this based on the details you've given, I don't know her side or everything there is to it) I would leave her. You sound like a nice guy, you'll work it out.