I've not read the middle pages so apologies for any duplication.
I run a food bank which also includes a pantry type setup (people come along, pay £3, and can help themselves to a range of items - typically two shopping bags' worth).
Yes we buy some things from the shops. In my case pasta, rice, oats from a wholesale supplier; beans and tinned toms from Tesco. I write eleventy million grant applications a year so we have money to do this.
Yes people do sometimes use us weekly/regularly rather than as a one-off. Not because it's fun getting food for free but because they consistently can't feed themselves/families well enough without us. Kids eat but parents don't, or they eat the cheapest crap there is, because £, or it's fine during the term but doesn't work during school hols. Or myriad other reasons. I promise, as pleasant as we try to make it, no one queues in the pissing rain for 40 minutes for food, sometimes with a child alongside, unless they need to.
We do redistribute things past Best Before but not Use By. Use by = safety. BB = quality. We do collect fruit, veg, dairy, bakery items, all sorts from major supermarkets and food businesses and redistribute it. We have to adhere to the law. So a UB product that comes in, with a same-day date - it needs to be frozen that day, or binned. But we have good processes to minimise waste.
This week people had beans, toms, pasta, tea, sugar, biscuits, instant noodles, a veggie ready meal and nine different fruits/vegetables to choose from.
NB - all services are different, so the fact that we do it this way doesn't make it universal.