So for the National event, each State is allowed One entrant? Are you talking about the collegiate event?
No, not the ACU-I event. It's the US Amateur National Championships. It's been sponsored / affiliated by the APA for something like 25 years. But it's not an APA event, so to speak. That is, the APA National Championships is a totally different animal than the US Amateur National Championships.
I don't know how many from each state or region go. Just like many National championships, there isn't a limit of one per area.
EAch person has to go through rounds of regional qualifying tournaments to get to go to the National Championships. I think if you just looked up the US Amateur Championships, this would answer any questions and is probably really as similar as you can get for what you're thinking.
In years on past, they would announce the name and the State the player was representing at the tournament (so I'm told by a few guys from that era). Now, not so much. Maybe they should still do it. Maybe I'll volunteer to do the announcing next year.
The trophy for first place used to be 6 ft. tall. That's the "impressive trophy" idea. Today's trophies are a little more airport friendly.