If you just bought it I'd highly suggest cleaning the jets completely. That doesn't solve the dying after releasing the brake, that's new to me. The clutch isn't engaged at idle, is it? Back tire doesn't try to spin constantly?
A lot of back flowing fuel could be a rich mix at idle.
Remove the carb, float bowl, and jets. Clean them using a very small wire and your carb cleaner. Reassemble. Check you fuel mix screw. Screw it all the way in, make note of how many turns in, just in case. Also, know the difference between the idle screw and the mix screw. After going in all the way on the mix screw, back it out 1.5 turns. That's a good start for a stock set up. It will take a few times turning it over to get fuel back into the bowl, unless you prime it first, I'm gross and do it by mouth. After getting it started and staying idling is when you can really tune the mix screw.
How did your plug look? It never hurts to get a new one, or three . Br8hsa ngk is what it takes.
Another check, before all that would be your vacuum line from the petcock. Might as well. I'm really just rattling off everything I would check.
The Super Nine is a fantastic bike, second to none in my opinion. But when you come across a neglected one they can be a pain, just like any scoot. Someone just posted their twelve year evaluation of one, the least amount of issues I've ever heard. I ride mine daily, rarely an issue. But I have went through a lot of learning about two strokes for it.