58 on a 14mm carb sounds right. that's the 2hp set up, which is correct for your bike. (You can check the manuals on mopedriders.org)
However, it should run with the airbox on. If it runs with the airbox off, it may overheat and also you will get all sorts of nasties in your carburetor and engine. Your airbox is probably gooed up. You can crack the airbox open and clean out the filter, but I recommend purchasing a new filter. You can custom fit a small cheap filter that you might find at autozone or you could purchase a maxi filter off of a moped shop (check the links page) If you go with a custom filter or a hiflow air filter, you will likely have to upjet (go to the next largest jet size- but get a bunch of different sizes to see what works best) Just make sure you aren't overheating, running too rich or too lean. If, after running around the block, you spit on your cylinder head or exhaust, it shouldn't sizzle.