RE: Engine not shutting down quickly
The typical places for airleaks are:
Carb - this is easily cured by removing the carb and applying some silicone to the o-ring and re-installing the carb.
Backplate - again, easily cured by removing the backplate and using some silicone.
High speed needle valve - you have a couple of ways to take care of this. Replace the o-ring, OR take a piece of LARGE fuel line and put it over the needle valve, tensionor spring an needle valve body. This is also good for repairing the needle valve when the spring tensionor breaks.
Front bearing - While this is not a common thing on TT (it is on SOME other brands that begin with a "T" ), it can happen. Your choices in this case are - send it back to the factory, replace the bearing yourself.
I would suggest trying the first 3 fixes. They are easy to do and will take care of the problem 99% of the time.
Hope this helps.