Food on table is IIRC ideally either for the Male/Female Manju to determine gender of offspring, or alternatively, raid effects (food on table won't be consumed, but their effects will apply to your NPC's during raids when placed on tables)
As for having people work on it: They're terribly slow at it, as far as I know. (But helps delay until having to refill)
When you interact with the foodbox, you should have the "eat" button, you can then also alternatively right-click on food items in your inventory to put into the foodbox, which will fill it up. (up to 1000 IIRC)