If you can find a local shop and knock out your classroom and pool work, you would only have to do your check out dives in Cozumel, then go diving on normal charters. I have dove with Blue Magic and Aldora and can recommend them both. Tres Pelicanos and Blue XT Sea have terrific reputations and a loyal following on this board as well. We dive Aldora for the larger steel tanks and long dive times now.
We have never needed a car in Cozumel. Frankly, I would not want to worry about the parking and liability on vacation. Maybe rent one for a day and explore the other side of the island, but cabs are cheap and everywhere. Town is full of one way streets that are less than marked, scooters zip around everywhere, and some/most rental insurance does not cover lost wages to the victim in an accident. Make sure you ask. You are in Mexico and things work differently if there is an accident....and it will be your fault. ISIS has a good reputation on here as a rental company. The navigation on my phone works fine if needed when we are walking somewhere new.
With the exception of La Perlita for lionfish and lobster, there are more choices for food within walking distance than you could eat at in a week. If you even want lunch after the CM breakfast buffet, it means you ate light for breakfast.
Prepare to have one of the best times of your lives!!
Safe travels,
Jay