We have two 50 gallon GE gas powered water heaters. The hot water output pipe has calcium deposits on it and is moist to the touch. The pipe insulation is also melted. The cold water supply is also moist. I don't think this looks right.
The tank is about 3 years old. I think the exhaust pipes were installed wrong as they are sloped down.
... a lot looks wrong here. With melted insulation, drafting is a problem. It is either negative air pressure in the building, pulling heater fumes back, or a partly blocked flue. In either case the poorly sloped vent makes it worse. ~~ I didn't like the look of the vent pipe to draft hood connection. The vent should not be crimped and should go over the draft hood. ~~ I'd rather see lined steel nipples or brass used in the tank, then to flex connectors, rather than copper pipe directly to the heater. This would help prevent galvanic corrosion. ~~ The water might be condensation or it could be a leak. You might want to uncover the pipes and mop up any water to see if you can find where it comes from.