I have a T who has an orientation toward the CBT styles.
I've never been given homework, but I think it depends on the person and their problems. Therapy of any kind should be individualized.

My thoughts are that if you don't feel like answering the homework questions, or you are confused, I'd tell her that at your next appointment. It sounds like the T's from your past, and especially the trainees, were not that helpful.
When you are dealing with free services, it's very difficult to get good services sometimes.

I'm always open and straightforward with my T when/if I don't like or don't understand something. Maybe you should try doing that?