Hello Tom,
This all sounds quite normal now.
The hot taps are likely to do that. The reason is the water heater has a non-return valve in its inlet and this causes a slight restriction to the flow into the heater. The pump can probably deliver more water than the NRV will allow to pass, so the pressure on the pump side will increase and can trip the pressure switch. as the water is still continuing to flow a little into the heater, this will drop the pump pressure and it will turn on again. As you describe this may happen a few times until the tank and pump pressure are equalised.
The other thing that can cause the pump to run momentarily is; as water heater cools down either when it is turned off, or you use some hot water, the water in the tank will contract. This will reduce the pressure in the tank, and this may cause the pump to run for a moment.
Something else you may need to be aware of, As the water heater heats the water in its tank, it expands. It can do this because the tank and its inlets and outlets are designed to trap a pocket of air at the top of the tank. as the water expands it pressurises the tank to a higher pressure than the cold water supply. Consequently, if you turn on a mixer tap, the hot water being at a higher pressure will be discharged first until the tank pressure drops and the cold water can also flow. The slight danger is that you may get a slug of hotter water than your were expecting. In some systems the additional compressible volume of the hot water tank can cause alternating hot and cool water delivery to mixer taps.
The solution is to fit a surge damper to the cold water pipes. This mimics the air volume in the hot tank, and minimises the surge effect.