The airport transfer company we recommend is:   https://www.entertainment-plus.net/cancun-airport-transfers/hotel-zone

They are the lowest prices anywhere and their service is great.  Moreover, while you are booking this you will see an option to add the grocery store run.  When you check this box they will take you from the airport, to the grocery store, wait an hour while you shop, then take you to the resort.  The extra cost is $30.  Please put in the notes: Superama Cumbres.  If you put that in the notes, they will take you to a huge grocery store in El Centro.  If you do not put this in the notes, they will take you to a smaller grocery store in the high rent hotel zone and the prices there will be about 20% more and the selection will be much less.

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Does the grocery store sell alcohol?  Yes, beer wine and spiriits.

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How much does the airport transfer cost:  You can have up to 10 people for $80 round trip for the whole group.  It will cost that much or less, depending on your group size.

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Is there any way to get groceries without going shopping?

Yes, the company is called cornershop, you order online and they deliver.  A guest used them recently and was very happy with their service.  Moreover, they can provide you not only groceries, but choose from a wide assortment of options, from bakery items to office supplies.  They will even bring you big bags of ice.  Link is: https://cornershopapp.com/es-mx/s/cancun