The first thing to do, if you haven't already, is to download and read the rules. https://barnhunt.com/rules/barnhuntrules_2016_final.pdf
This is the current rulebook. The updated rulebook will be out soon, but until then, these are in effect. Also, don't forget to register your dog with BHA, since they need to have registration number to compete in a trial. That's done online, and you get your number right then.
Instinct is a single pass/fail run. A dog can compete in Instinct until the have their Novice title. Novice requires three passing runs. If the club allows move-ups, and Novice A isn't at its limit, then you can probably move up, but sending the Trial Secretary an email making sure about that is a good idea. If they allow move-ups, and you want to give Novice a try, then yes, bring money.
According to the NASDA website, they were just formed in 2016, so yeah, they are pretty new. Looks like they are mainly in the western part of the country right now. Their Trailing and Locating looks kind of like RATS! Canada's Brush Hunt, from the little bit I read of the rules.