1. The possibilities are perhaps to learn coping strategies, to work on your relationships, to address faulty/defeating thought patterns, to talk about things you've been afraid to talk about, to process traumatic memories, self-care goals, etc.
2. Your goals can be both short term and long term goals. Therapy goals are very flexible, in my experience. I had a goal that I wouldn't be crying every day. That goal wasn't about will power/forcing happiness; it's just a way to acknowledge that I hoped therapy would help me to feel better over time.
3. You can expect something to happen right away, but it just as likely may not.
4. If you're over thinking it, try not to worry about #2 and 3. For ptsd, now I am at the point where my goal is to have a complete framework in my mind that combats each effect of ptsd. When I have a symptom, I want to be able to recognize it right away, and perform my counteracting thought/ behavior to restabilize.

Just my two cents! Good luck with your goals