You didn't give a model of the fryer although you noted motor specs. If a gas fryer, then the motor is a 120v. If an electric fryer, could be a 120 or a 208 - I've seen BOTH on electric models. You must get the right one because the motors aren't designed for low or high voltage rewiring. It's one or the other. That 8261756 number in your specs is Frymaster's part number for a 208v motor.
According to the picture, that motor is a 208v, although that detail isn't given in the e-bay ad.
I can't tell that from the picture. The reset is mounted on the back of the motor and IS susceptible to damage if not properly packaged. Since there's no shaft, only other vulnerable area is the mount foot - which isn't an issue.
The reset CAN be ordered and replaced. Gotta solder the wire connections.
Last note: You should've separated the motor from the pump. If you found oil migration from the pump seal, replace the pump too. Otherwise that motor will fail again soon due to oil and/or moisture migration into the motor.
If you look,there are three pictures of the motor .One is of the back of the motor.