Question.. Is it a slow drip while the water heater s heating or a fast and constant flow or a drip all the time.
The first problem (A slow drip while heating) but no leakage when the heater is off but the water pump is on may be normal operation of the valve. Drain the water heater and see if that fixes it. More on that later.
The other two are problems.
And yes, it is a very standard hardware item.. Make sure you take the old one with you as they come in two sizes.
Now, the drip when heating,, NOTE this can also happen when on city water in some parks if you DO NOT have a proper pressure regulator.
Normally the water heater is partially full of air, and part of water. This is normal. and nothing to worry about.. over time the air is absorbed into the water so the air cushion at the top of the tank shrinks.. Takes a few months before it's noticable and in my case the first warning is if I'm running on stored water, when the ice maker cycles it takes 4 or 5 runs of the pump to fill the tray.. A fresh cusion of air takes only one run of the pump to fill the tray.
Many water heaters have check valves in the cold water inlet to insure hot water does not back up into the cold lines.. If yours has this then as the water heats and expands it has no place to go.. ALL motor homes and trailers have check valves on the water pump and city water inlet.. It takes a lot of air chambers to absorb the amount of expansion.. not all rigs have it.. Thus the drip, till you restore the air in the chamber.
Finally.. If you are on city water WITHOUT a regulator.. And the city water pressure is too high then even less expansion (or more air) is needed cause you are starting closer to "Drip, Drip" time.
Normal pressure in a park with it's own wells is 50-60 PSI
City water is often closer to 80 PSI and in one park I've been in I saw it hit 120, They warn you on check in that it hits 120.
In one park with its own well I've seen it break 100, The pump was 'Waterlogged" so I can not tell you the actual peak pressure.
What's waterlogged? Well, the well pump pumps water into a pressure tank, like an "Accumulator" tank (Optional on motor homes and trailers) this has some kind of pressure absorber in it, may be a diaprham with spring, may be.. An air cusion, just like the water heater.. And yes, the same thing happens to this tank.
How to fix it.. Well, two ways, 1: The well pump has a device to inject air into the water stream normally,, 2: Drain the tank and let it re-fill with air, then pump it up again.... Done that many times.
Home is where I park it!