there is no supermarket close by, there is one along the way from the airport to Westpunt at Tera Cora, the supermarket is called California. It will not be up to your usual standard, but shopping is okay there. No exclusive products like French cheese or a large wineselection though.
There is also a very small 'supermarket' (more toko which means foodshop) along the way from Kura Hulanda Lodge to Soto, it is about 5 miles from the Lodge. If you look at the map, you'll see the road in Bandabou (west side of the island) looks like a lasso, Soto lies on the south side of this lasso. You can't miss it. It is a very simple neighbourhood toko, but for things like juice, tea, coffee, bread, cookies, etc it will suffice.
You can pay almost everywhere in dollars, the rate is 1.75 antillian guilders to the dollar. But often you'll get change in antillian guilders.