It should specify on the board at the front. I think most go to the local Foodbank- at ours, we have a volunteer who goes to every week and collects all the donations and takes them down to the Foodbank.
I think some supermarkets donate to Fareshare, which is a slightly different but equally worthy cause (they tend to distribute surplus supermarket food to places like soup kitchens, day centres for vulnerable people etc).
EDIT: and I’d say yes in normal circumstances, but we usually get loads of chocolates, sweets and so on around Christmas, and they have a shorter shelf life than other items.