Im also new to this community and I don't normally comment on profiles, I just read the conversations to pick up tips but the experience you are having with your friend sounds really similar to the one I'm going through with my older brother. The biggest advice I can give you from my own family's experience is stay positive, but also stay realistic. My brother is intensely independent and always knows exactly what he's going up against so he doesn't need anyone around him trying to candy coat things or to be all rainbows and sunshine all the time. This obviously goes hand in hand with honesty and I always found if I didn't know what to say, or if something he blurted out left me speechless, telling him I didn't know what to say was okay. Often a hug was as good an answer as any.
In terms of the more serious questions and her attitude towards giving up, have you looked into depression? Or talked to her about it? To my family it is really important to keep my brother optimistic and keep him from feeling beaten down by the constant drone of treatments and tests. I know a lot of doctors have also pressed upon my family the importance of a good outlook.
There are a lot of good resources around, my family has found 'cancer compass.com' 'chemocare.com' really helpful and the canadian cancer society has a page of information dedicated solely for caregivers as well as an awesome online forum (cancerconnection.ca).
I'd love to talk to you more. It sounds like we're in pretty similar situations.