This is a complex problem, and it's going to be difficult to provide an accurate answer without inspecting the equipment. So this is going to be more like a few comments, than an actual answer.
Water heater
I'll start with the water heater.
Old units aren't efficient
If the unit is older, it's likely not performing at peek efficiency, which is wasting energy. Updating the unit could save you money in the long run.
Tank heaters waste energy
No matter how much hot water you use, the heater is turning on from time to time to heat the water in the tank. The only way to eliminate this waste, is to install an on-demand unit.
Fuel source cost
Depending on the costs of different fuels in your area, switching fuel source could save money. Installing a gas fired on-demand water heater, could save you money long term.
Fireplace
If the fireplace doesn't have a fan, that is blowing heat into the home. You're quite possibly drawing more cold air into the home, than the amount of air the fireplace is heating. By using the fireplace, you could be blowing money out the chimney.
Also, the cost of wood is typically quite high, compared to other fuel sources.
Heat pump
Heat pumps use a lot of electricity, which in many parts of the country is an expensive fuel source. In temperate climates, heat pumps make sense because they're not typically used much. In climates where the temperatures often drop below freezing, heat pumps are virtually unheard of. This is because heat pumps aren't so good at heating homes, and often have to rely on supplementary electric heating elements.
Use the furnace on cold days
Since you have a gas furnace in the home, you can use that when the heat pump can't keep up. Depending on the local gas price, this could save you some money. In most dual fuel systems (like yours), if the heat pump can't keep up it shuts down and the furnace runs instead.
From your description, it sounds like the furnace and heat pump are running at the same time. This is not a good idea, and can actually cause damage to the system.
You'll want to configure the system (or have it configured) so that when the thermostat switches to auxiliary heat, the heat pump shuts down and the furnace kicks in.
Without actually being at your home, it's difficult to diagnose the problem. You might want to have an HVAC technician come out and evaluate the system, to help determine if you're wasting money.
I would think electrolytic corrosion to be unlikely due to the intermittent nature of condensate flow and the fact that the brass fitting is isolated between nylon and PEX.
Your thoughts around acidic condensate are intriguing. Boiler feed water for industrial steam systems is treated with inhibitors to prevent yellow metal corrosion in the condensate collection systems, and industrial closed-loop cooling systems are treated for the same reason, so it is a known fact that yellow metals are susceptible. Pure water easily absorbs carbon dioxide just from being exposed to air, so the gas-rich environment of the combustion chamber may be accelerating the process.
I would replace the nipple with a plastic component, that should take care of the issue either way.
Best Answer
I think that might be an old coal burner with a dome heat exchanger on top (also known as a radiator).
I have never seen or used one of these in person, but there is some information about this stove type sparsely spread around the internet. I understand they are roughly 1940s vintage.
Consider this photo of a competing Wards model:
Ash tray is the bottom door. Coal is added through the middle door and air inlet is controlled at the middle door and/or bottom door. The top end is a heat exchanger that circulates flue gas to the center dome, then to the front part of the doughnut, around the sides, to the back, past a manual balancing damper at the flue connection and then up the chimney. The manual balancing damper at the flue would be needed to manage airflow in concert with the intake. I believe the front door on the dome is there for cleaning and remains closed during normal operation.
This stove is not likely to be efficient by today's standards because it is not equipped with a secondary burn chamber.