Regarding the psych eval, I'm pretty sure it depends upon the State you're in. But in most, based upon what I've read, they will evaluate you and then likely release you without treatment if you are not posing an immediate threat to yourself or others. In some States, this will be in the ER. In some States, it's in a psych ward.
You speak about these things in absolutes, like you're an expert, as though because you drop them off you know the entire process for your State and every other. I'd love to hear from an actual expert on the subject. As I said before, I am almost sure that there were some ER nurses posting to the boards here.