Do my cashiers see the whole menu on the POS, or only the dishes I choose for them?

They see every dish that is on sale, in the order you arrange. Settings → Arranging the POS changes the order of the tabs and puts your busiest dishes in the Most sold tab, but it never hides a dish and never changes a price. To take a dish off the POS, use the Available or Sold out switch on the Menu page, or let the kitchen mark it off from the kitchen screen. A dish with a stock count greys out on the selling screen by itself the moment it runs out. So the POS shows what is for sale, and the Menu page decides what that is. The Menu & inventory tab in the docs covers the sold out switch.