The airbox usually will accumulate a bit of left over residues from the crankcase, so it is somewhat normal. If the drain hose from it is blocked up (*this goes down to the middle bottom of the bike along with a few other vent hoses, and some are capped normally*) the amount might be more than normal. Check that drain hose then dry out the box and you will be okay.
As to the petcock, the little filter on it is hard to see, so I'll try to find a picture. It would help if you'd put your bike year and model in the signature line and edit your profile to give your location. Makes it easier for us to help you.
Joel in the Couve