Hi there, nice find on the NC50's!!!
These are actually regular scooters and not mopeds - called nopeds by the enthusiasts since they don't have pedals ha - and would need a scooter/motorcycle type of license and plate. Make sure you figure that out before going on actual roads cause it can be an expensive ticket.
As far as those, I have owned 3 and they are extremely reliable once you get rid of the stock carb like you did. The original one is super finicky and it has to be a perfect day, with just the right a amount of moisture, sun, wind velocity blah blah blah for those to work ha.
Since you removed the original one, I would recommend not throwing it away, you can easily sell it for good money since there are lots of followers who will pay top dollar for original parts.
All the ones I had I removed the oil pump mixer and just mixed my own fuel. I didn't want to trust a piece I couldn't really see working and it is free to do. Also I pretty much kept them original, so I'm not the best to answer your exhausts question but I would recommend going to mopedarmy.com and asking around to see what others have done.
Post some pics