1) The best way to prepare is to write down the main things you are concerned about and any symptoms. Basically things to prompt you.
2) It depends on how much you have to say and on the psych. My psych talks a lot and my assessment lasted 2 and a half hours. Could be shorter or even longer I guess depending.
3) They will ask you about your past, your childhood, your symptoms, how your problems are affecting your life, your current situation, where you live, who you have supporting you, family, past experiences that might have caused issues, whether you work etc. Basically they will want to know your past history, any possible causes for your feelings and how your mental health is impacting upon your life.
4) Depending on diagnosis but I would imagine you would be referred for some sort of treatment. Obviously the kind of treatment would depend on your diagnosis. They may prescribe medication or they may not.
5) If they say they don't think you have a diagnosable condition then nothing happens as such. They will probably discharge you, or perhaps tell you to access counselling through your GP. You could seek a second opinion though. I am not sure how private practice works tbh.
I would say it is likely they will want to help you though. Try and be as honest as possible. Hope it goes well.