There is a wealth of info (much of it current) here on ScubaBoard about Cozumel. One way to find some specific info is using the search feature in the menu bar on the upper right side of your screen - at least that's true for my laptop and iPhone. Another way to search is to click on some of the "Similar threads" section which is below the last post of your current thread.
That said, here are some brief comments to help get you started.
What medium price all-inclusive is good? Do any include Scuba in the package?
Cozumel is all about the many options available to divers. There are AI resorts that have dive ops on site that you can set up dives with - some have had occasional specials that do include diving. Some resorts/hotels are mandatory AI, while some are optional. A few years ago, we stayed at an AI optional resort in the north zone that had a dive op (shack) onsite. We paid $50/day for the AI and the way the diving worked was to take a taxi all the way to the south where the dive ops dock was located, a short boat ride to the dive sites. Knowing what I know today, if I stayed in the north zone, I would dive with a different op located at a different resort in the north - I became a fan of the fast boats that get you to the marine park, which has the majority of dive sites, faster than boats that are actually closer to those sites.
There are dive ops that work in conjunction with different resorts/hotels to provide "stay & dive" packages and, I believe, some of those may offer at least breakfast, but not sure about the whole AI meal plan.
Prices on AI vary, so maybe you'll get some good advice on that. I will say the nicer beaches are in the south.
What Dive equipment should we bring?
A question that will get you personal preference answers. Dive ops can rent you equipment for the days you dive - many will hold that gear for only you. You can also bring your gear as most ops provide a place to keep it for you. I've seen long time divers in Cozumel who do both. Although I always take mine, the only thing I really need is my mask as it is prescription.
What are the water temps and viz? What is the diving like? How deep do you usually go?
Agree with
@rick00001967 about the conditions. Last fall every 1st dive of a 2 tank dive that I did was 80+ ft. Second dives could be 30-60 ft. You should be comfortable with drift diving and dives can easily last 60+ minutes.
What are the best dive locales we should shoot for?
Chances are you will dive in the marine park where all ops dive, especially if you're staying at an AI resort/hotel. That's not to say you can't or won't do something different, but the marine park is really big and has some really nice dive sites. Many DMs ask where people on the boat want to go with a majority rule as long as conditions are good.
Should we rent a car the whole time?
Again, personal preference prevails. As most AI's are not near town, it will depend on what you hope to do/see. You can find a thread of pros and cons of renting a car. We rented a Jeep for 24 hours - about $110 not including gas. Drove around the island, avoiding town - took in the Mayan ruins and the east coast, stopping at Coconuts Beach Bar. Taxis are cheap, $5-8 one way depending on distance.
Going to town at least 1 day to walk around, eat, and shop probably should be in your itinerary.
What other non-dive activities are good.
My opinion only, there is not a whole lot to see on the island - maybe things to see, but are they really worth it? If you go to the San Gervasio Mayan ruins, it might be worth it to use the guide that will offer their service. A different activity might be to take the ferry to Playa Del Carmen and spend the day shopping or do an excursion which leaves from PDC. Xel Ha water park was great fun although we did it when we stayed in PDC.
Following is a link to info I put together on dive ops in Cozumel. It might give you some ideas of where to stay or dive. Have fun!
Finding a (Best) Dive Op in Cozumel