EDITED

You don't need a head gasket.

Water is a byproduct of just about anything burning including gasoline, wood, natural gas, propane, etc. That's why you have water out of the tail pipe. That's not a problem. Water in the spark plug tubes could cause the wire to send the voltage through the water instead of the plug causing it to run rough. Just dry it out. Also, in the mean time, you will be running really rich and may nead to clean or change the plugs. I've also heard about water getting into your air intake when a car goes through rain or puddles. One guy said that the rough idle went away with a few days. I would at least look at the plugs.

As for the idle bouncing...I have the same problem and haven't figured it out yet. My idle screw is all the way in too. I doubt it would cause a problem unles you "tighten" it. Once a screw makes contact on the throtle or a carb., you don't want to force it any.