I haven't ripped one apart, suspect its a thermally actuated overcurrent device.
Others may have better info. Not a fan of removing it. If you are following the script suggest you put the fuse where you can get at it at least.
Exactly.
It's called a thermistor.
It's there to prevent overload damage to the motor/circuit.
I wouldn't remove or bypass it.
Upgrade the feedwire to the motor,yes.