That’s a lot of questions. I hope I am able to answer most of them...

I’m not sure how I would find out unless they tell me. Assuming they tell me, I would never think less of them, and I would attempt to help. I am not a mandatory reporter of student mental health issues because I’m not a licensed mental health practitioner. (Professors at my university are mandatory reporters of sexual violence and gender misconduct.)

If they are an imminent risk to themselves or others, I would recommend the ER. If not, the student should go to the counseling center. I have personally escorted two students there.

I don’t know when emergency contacts are notified.

AFAIK, a student cannot be forced to withdraw if they want to stay and are not a danger to themselves or others although it might be recommended. The student could take a leave of absence, and the reason would only be known to the relevant parties. I know of a student who had to complete an inpatient program and an intensive outpatient program as a condition for returning to classes. Every case is different.

If the student drops out, why would the authorities be notified? Do you mean police?