We do check bags. The procedure is not all that complicated for retrieval of checked bags - they have them all set aside by airline - you simply find them and continue thru the USA process - then give them back to the airline employees waiting for them and they handle the rest.

The lines will be long on Saturdays and Sundays.

There are shops after the Aruban portion of the inspection and also shops after the USA portion so you will have the opportunity to make purchases if you wish.

I forgot to mention you did ask about grocery stores - there is a small mart in the Alhambra Casino complex, opposite the ABC where you can get some basic items but of course the larger market will offer more selections and lower costs. Ling & Sons (the big market) is one of the few places that give change in local currency, you can use it or turn it in to their customer service desk for US.