Everything you say to the therapist/doctor doesn't leave the office due to HIPAA laws. Therefore, the door should be closed and the session private. The professional should not speak about your case to anyone without your written consent and signature.
You will be asked if you've been depressed or anxious. Whether or not you've had thoughts of hurting yourself or have committed the act of self-harm. You will be asked if you've had thoughts of suicide and whether or not you've thought of a plan to carry it out. If you admit that you do hurt yourself and you've had thoughts of suicide, the professional has an ethical obligation (if they find you to be a danger to yourself or others) to inform the proper authorities about this and possibly have you committed. Usually, unless you say you have a plan, however, this will not be done.
You have the right to ask about your diagnosis if you so wish. You also have the right to ask about your treatment plan and what is on it.