Thanks brobergsweden - that really means a lot.
Just to update you, we're speaking more regularly now, maybe 3-5 times a week, just over Facebook. I'm still worried she thinks I'm "too needy" (since I escalated things too quickly), so I'm making a conscious but subtle effort to give the impression I have things to do other than talk to her, and will often leave the conversation to do something before she does. I also wanted her to have space so she could think about what it would be like to not have me in her life, then when I speak to her (and it's always me initiating conversation. She hasn't since we started speaking again, but in fairness, rarely did before that), remind her of things we did that were fun. I'll keep the conversation away from emotions/feelings or negative things, and try to keep it exciting.
I've asked her a couple of times if she's free to call, but she overlooks the question or suggests there's a better time when she's less stressed from writing her essays before a deadline coming up in a couple of weeks.
She complains frequently about uni work stressing her out. For example, today when we were talking about Christmas and drinking after she sent me a picture of her Christmas tree (a positive thing I thought) she said:
"I wish I had time for drinking. Once I hand in my last assignment I'm going to hibernate in an alcoholic sleep so that I don't feel depressed cause of Christmas
"
I just replied very neutrally:
"You have friends around, they'll look after you. Go out and have some fun and meet some more people
".
I always get the impression when speaking to her that she isn't happy and is trying to remain positive. Whether that's her way of keeping guys interested (we feel protective over her given her situation) or whether she's just genuinely having a rough time - I don't know, so I'm not acting on it in case she blows me off and I look "too needy" again. Despite that, I do care a lot about her and I don't want her to feel like that.
This might be a minor thing, but I want to mention it anyway. Whenever we speak on Facebook, she seems to overuse ";)". For example, she'll say "How are you?

" or "Hey

" or "Nope (when answering to plans for the weekend). Work work and some more work

not that I mind it". If ever I've used this smilie (which I don't often. I think girls see it as creepy and/or unnecessary), I'd use it because it's flirtatious or to suggest a positive underlying message to what I've said. For the same reasons as above, I just reply neutrally in case it's not intended in the flirtatious way I naturally interpret it.
I have thought about going over to see her. In fact, I've thought about going over to surprise her for New Years Eve. She'll have finished her uni work, but I'm not so sure that's a good idea just yet (correct me if you think I'm wrong). The fact that she has more or less declined speaking to me on the phone gives me the impression she doesn't want to see me just yet. If we get back to doing that more regularly, I think you might be right - I should go see her and I should spend more time with her.
Do you think I'm right to go about things as I am? Would you change anything I'm doing?