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.
The answer will depend on how much temperature drop/rise there is inside the ducts. A two stage cooling system means that the heatpump will either drop the air return temp a little bit (stage 1 is running, half cooling) or it will drop the air temp a lot (stage two is running, full cooling). Either way the fan moves the same amount of air. In stage 1 mode the net effect will be for it to spend more time with the fan on, since to hold say 70F it will have to spend a while pushing 65F air through, vs a single stage system that puts out 60F air which will get back to setpoint faster. More air circulation (assuming its all a nice 65F) should actually be better for comfort in your restricted upstairs area vs spending a short time blowing 60F air until the downstairs is comfortable, leaving the upstairs without much time to get cooled air.
If the ducts are soaking a lot of the cooling up (i.e. the downstairs is getting 65F air but the upstairs is getting 68F air) then no, the first stage of a two stage unit will not give a lot of comfort and a system pushing colder overall air (i.e. single stage) all the time would be preferable.
In any case (if you get this system or not) most ducts, even in older homes, have some sort of internal damper to control flow to each run/room. These might not be accessible if you finished your basement and covered them all up, but that's for a different question about exposing louvers and patching sheetrock ;-). Further, your vents in each room should have a shutoff (not preferable vs in-duct damper, because it's noisy) which would allow you reduce the airflow to the downstairs rooms. This would be the solution if you find that running the system just doesn't get the upstairs rooms comfortable. Start by reducing flow to the one or two ducts closes to the thermostat, and continue until your system runs long enough to cool the upstairs without leaving any of the first floor rooms too frigid.
edit: grammar and clarification
Best Answer
Heat pump + hydronics is a fantastic combo, provided you can get an air handler that supports it
While you are correct that the combination of a heat pump with hydronic backup heat is uncommon, it is not bad by any stretch of the imagination -- when an efficient boiler is used, it will beat a forced-air "dual fuel" setup any day of the week when it comes to overall fuel efficiency as the hydronic setup can run the hydronic coil at part load to make up what the heat pump can't provide, something a forced-air furnace can't do, and is far easier on your house's infrastructure (and the electric grid!) than all-electric setups are, especially in cold-climate areas.
However, due to this rarity, not all heat pump manufacturers provide air handlers that have hydronic coils factory fitted in place of the normal electric standby heat. I am not certain if Bosch provides that option; if not, you will need a skilled HVAC shop's assistance to field-fabricate or field-modify an air handler for your setup.
You probably want a water tank somewhere in your setup though
However, on the hot-water side of the picture, you probably do not want the boiler to try to serve hot water loads directly -- this is inefficient as it forces the boiler to try to balance between competing needs. Instead, the superior approach is to use an indirect tank hot water heater that runs as a hydronic zone off the boiler, with the water in the tank is heated from the boiler water via an internal heat exchanger.
A high-efficiency boiler and indirect tank is as efficient as a good gas water heater, while providing excellent longevity with the availability of stainless steel or cement-lined tanks (vs the normal glass-lined steel tank) and superior capacity due to the extra heat exchanger area compared to most gas water heater designs. It also avoids the comfort issues that are possible in tankless setups (such as the "cold water sandwich" problem), and requires less peak capacity from the gas service.