If the plaintiff redoes the small claims case as a trade secret violation (idea submission law) then indeed small claims might hear it. However, the question says the plaintiff "emailed it to everyone", which sounds like loss of trade secrecy. So, no patent, no trade secrecy, no copyright reg, makes plaintiff grasp for straws and may lead to success in a motion to dismiss. Indeed, a NY IP lawyer should have the answer or be able to research and find the answer. Problem is, this small case is not worth an IP attorney's time.
I agree the amount in dispute makes this un-economical to hire an attorney. But idea submission law [implied-in-contract law] is wholly seperate and fundamentally different from trade secret law. If I was the small claims judge with a plaintiff in front of me claiming he created a work for Purpose #1 but either wasn't paid for it or that now it is being used for Purpose #2 then I would characterize that dispute as being founded under contract law. Not copyright nor trade secret law.
Could be. It's too speculative due to skimpy factual description in the question to know. My thought is a motion to dismiss forces the plaintiff to either drop it or spend money and time and that dropping it may be plaintiff's choice. Also, if the Judge is busy, or the Plaintiff a bother, the Judge may latch onto a motion to dismiss to dump the case and move onto something more interesting.