You're being an awesome friend - and you're doing all the right things :) but dont expect it to get better in 5 weeks. That sounds horrible, but depression often lasts for a while. To deal with/get over depression its necessary to understand and overcome what has caused it. That's where a psychologist comes in handy - however, it can be difficult to find the right one. Perhaps your friend might prefer to talk to someone who is young and more like a friend, or maybe someone who is more like a motherly figure..? I have no idea. The most important thing is that she trusts the psychologist.
Its really important that your friend gets professional help. (btw are her parents aware about everything?) I know from personal experience that some sessions with a therapist can be upsetting or make 'you feel worse.' Talking about upsetting or uncomfortable subjects can be very confronting, nonetheless it helps in the long run when learning different perspectives, thinking skills and ways of coping. Perhaps your friend has just never met the right psychologist? Tell her to give it another try.
Another issue is that she might have low seratonin levels, and that certainly doesnt help when trying to make decisions, with sleep, learning and thinking rationally. Has she considered medication? This can make therapy sessions easier; treating the symptoms while the individual deals with the issues that led to the illness.
I dont really know what else to say. Id totally recommend some therapists known to do well in their profession but i live in victoria - i have no idea where your friend lives.
The main thing is that your friend wants to get better, wants to stop feeling like absolute crap and whatnot. Its not going to happen unless she takes the steps to getting some help. (and the fact that she isnt enjoying what she used to love defintely points to depression signal :/). I really hope everything goes okay. If you want any more advice or anything this is my email 7differentways@gmail.com . Im no expert, im just an 18 year old girl, however ive been through this myself, and i got out of it and im much better off than i was :)