Can I refuse treatment?

In America: Yes, up until the point where the patient is declared to be incompetant or temporarily incompetant. At this point, whoever is acting as their personal representitive (e.g in loco...

Yes they do. Most likely, a paramedic will then have them sign a waiver claiming that they refused aid. This prevents anyone from being responsible for them.

A psych patient, I think, can refuse getting a treatment like any other patient, unless he endangers himself.

No. As long as you can make the payments for all the fees and hospital charges, they cannot refuse treatment.

Any patient, being of sound mind, and not under court order can refuse any medical treatment.