Here are your parts includes a wiring diagram but it is poor quality.
Replacement parts for FRIGIDAIRE GSE746RHS0 Gib(v0) / Dryer | AppliancePartsPros.com

See the attachment for a more legible wiring diagram.

I also noticed the thermal limiter is burned, would it not work if the thermal limiter is burned?
Yes a blown thermal limiter will kill power to the motor.

If it is open be sure to check/clean your vent system as it is the most common cause of it blowing.

If the vent system is clean and the vent lovers open then:

Check the heating coil.
Unplug the unit and both wires to the coil.
Check it with a meter, should be around 10 to 12 ohms.
Then check from each side of the coil to the case/frame, both should be infinite ohms (open). If not the coil may have sagged or broken and is touching the case. This can cause it to run on high and the thermostats cannot regulate it so the thermal limiter blows.

There are several other things that could cause the limiter to blow.