You should not use a "naked" L7805CV. That voltage regulator requires a couple of capacitors and a resistor in order to build a functioning voltage regulator out of it. You should be able to find instructions online for how to build one.

That said, 9V is a good unregulated voltage to provide to the Vin line on the Arduino. Its built-in voltage regulator should be able to regulate that to 5V quite well, even with "bobble" caused by motor. (The built-in voltage regulator is able to handle input voltages from 7.5V to 12V, although if you feed it 12V and draw a lot of current out of the 5V line you may have overheating problems.)

You should also use a "logic level" MOSFET that can be driven with a 5V gate voltage.

You should not use a "naked" L7805CV. That voltage regulator requires a couple of capacitors in order to build a functioning voltage regulator out of it. You should be able to find instructions online for how to build one. Search on "L7805CV circuit" and you should find quite a few sample circuits.

That said, 9V is a good unregulated voltage to provide to the Vin line on the Arduino. Its built-in voltage regulator should be able to regulate that to 5V quite well, even with "bobble" caused by motor. (The built-in voltage regulator is able to handle input voltages from 7.5V to 12V, although if you feed it 12V and draw a lot of current out of the 5V line you may have overheating problems.)

You should also use a "logic level" MOSFET that can be driven with a 5V gate voltage.