Not a huge deal if you don't have a hose attached to the nipple. It basically just means that fuel will dump on the engine as opposed to the ground. As long as it's not dripping, it is fine. If it drips for a long time, fuel will eat into stuff, cause discolouration etc. Tubes are cheap...
You're having trouble because you didn't properly winterize your bike. Tank should have been full, and fuel stabilizer should have been added. Hopefully you don't have bad condensation in your tank or any rust that formed. Here is a thread on how to winterize your bike for next year:
http://honda-cb750-s.456789.n3.nabble.com/Winterizing-the-bike-td3433181.htmlYes, as long as the black smoke clears it shouldn't be an issue. The carbon buildup would be caused by running it really rich for a long period of time.
I would start with seafoam and good gas. Giving the carb with a stuck float a little tap might also cause whatever is causing the float to stick to resolve.
If it were me I would pull the carbs and clean them, but I like really clean carbs and a very well running bike.
1981 CB750K with 900 cams
90K KM's, rebuilt head, rebuilt carbs, upgraded valve stem seals
My wife's recipe website that I'm trying to help promote:
Strawberries for supper. Yes, I am a lucky man.