2) Would you rent a car in Cancun and use it everywhere or would you use a scooter in Cozumel and the bus everywhere else?
Unless you are an experienced operator of two wheeled motorized vehicles, I would emphatically recommend against renting a scooter. Scooter accidents are the leading cause for emergency room visits by visitors to Cozumel. They are deceptively easy to operate, but more importantly they are also very easy to lose control of, especially if you are a novice. I have had one friend killed and several people I know severely injured on rented motorbikes.