One of the first things a good counselor will do is to make sure you are safe.
There are different variations of the types of questions they will ask, but the majority of them will revolve around your mental health and how long you have been feeling this way. They will also ask you questions about your background.
More than likely a counselor will not be trained to give you a depression screening; they might have you talk to the school psychologist. However, if you feel more comfortable with the counselor you can ask that they sit in with you.
Everything you discuss with the counselor or the school psych is confidential. The only time that it is not, is if you tell them you plan to hurt yourself, hurt someone else, or if you are being hurt by someone else.
Remember these people are there to help you. Being as honest as you can help them give you the best possible care they can.
If you are feeling depressed, reach out to someone. You can also try a couple of other resources that are 24/7:
Thanks for reaching out and I’ll be thinking about you.