Good job with the photos, showed exactly what I wanted.
You might have an extra temperature sender for whatever reason.
Your mystery hoses were definitely for the water heater. Someone plugged the inlet and outlet, removing it from the loop. I can't tell you why, maybe they just never used it but I would suspect your water heater is done for and rather than replace it the previous owner just eliminated it from the circuit.
I've attached two diagrams, showing the old and new fresh water pumps. The new one shows which serial numbers it applies to. You'll be able to easily figure out the correct way to set up the supply and return lines again with it. Not sure what to say about that extra temp sensor though, it might need some investigation.
Also included a photo I found online - while I absolutely don't condone the hard pipe used there due to vibration issues it shows the supply and return attached.