LM393 is a comparator, not an opamp. tying comparator inputs together may cause oscillation, so they use inputs that will always be significantly different.
BTW the reason the diode is where it is is to avoid it needing to be big enough to carry the motor current. If connected backwards, the MOSFET's body diode would turn on, & the motor would run (backwards), but the diode protects the rest of the circuit.
The 10R provides some filtering, and may also be intended to act as a fuse, in case of a fault with the control circuit drawing excessive power.