Yes thats the one, temp gauge sender is just a single wire and has a much smaller sender

Yes the CTS is one of the most important inputs as the info it supplies will be used to determine the base level of fuel injected from freezing to boiling, I should think if you disconnect this the ECU will think it's very cold and fuel accordingly!

The hunting can also be caused by a bad TPS calibration as could the overfuelling I should think!

Martin