Cut off switches
 

Do certain tracks or race courses demand cars to have engine/fuel cut off switches if they fall into a certain category? I'm assuming the category is if your car runs a certain time i.e. specific horsepower rating.

Yes, in fact all NHRA tracks require a manual shut off that kills the motor and disconnects the battery. Doesn't mean they will always insist though for daily drivers.

Any drag racing that adheres to NHRA rules will require a cut off if your battery is remote mounted. If it's under the hood, no switch is required.