Answered: What is considered a motor?

In rule <R11>, it states that

So my question is “Does a non-functional part of a motor still count as a full motor?”

It is clearly established that motors may be taken apart to change the gears for different ratios/speeds (<R15>iii). Also many teams choose to leave out the screws holding the motors together in favor of zipties to make servicing or gear change quicker and more convenient (in past Q&A).

What happens if, for example, in an effort to remove a motor deep inside the robot, the gold motor screws strip and you are unable to remove it without cutting the metal it is attached to? Would it be okay just to leave the top (bottom?) of the motor shell in place, and put a new motor in the desired location? Would the unusable partial shell still count as a motor, or could it be considered a non-functional decoration? I know you are not allowed to modify electronics, but taking apart the motor without modification is allowed.

No, motors cannot be used as non-functional decorations. Please see the following Q&A post for more detail:

https://vexforum.com/t/answered-vrc-motor-casings-and-motor-limit/42455/1