Condensation Or the tank rusted out
the heater core has got a hole in it or your top has a hole init. If the water is green it is your heater core. if not it is your top.
"hold water" and cause edema.
No.
a bad water pump could cause low heat. The heater uses the coolant from the pump to generate heat.
Only if if has a leak.
The installation of a solar water heater will cost between $250-500.
Yes
It rusted out
Only if installed incorrectly
There is no relationship between them. a bad heater core will give you no heat, and maybe water on passenger side floor. A bad head gasket will cause oil leakage and lack of compression.
If you have a new pressurised water system there is a possibility that the added water pressure could cause a leak.
It is most likely the water heater. More specifically, the anode in the water heater likely needs to be replaced.