Temp Guage

No you cannot interchange them. The one that came with the fan works like a on/off switch and is either on or off depending on the temperature. The one for the gauge works like a thermometer where it is always on but is basically a rheostat and continuously sends voltage readings to the gauge. That voltage varies with temp.
You could run both though independently. If you could run a t-fitting but that wouldn't look too good but would work. Or find another to mount one of them.
You can go to a parts store and get a radiator mounted thermostat for the fan. It mounts between the fins on the radiator and sometimes are adjustable for different temps to kick on.

Yes you could as long as it clears the thermostat. It might be worth pulling the housing off and threading the sending unit in and then putting the thermostat in place to make sure the is no interference.