IMO, the food waste bin is for things like bits of meat, scraps with protein. We have a compost bin (rather than a food bin like yours) and certainly yes, my raft of banana skins goes in there. If I were you I would put all my fruit and veg scraps and peelings in the garden waste bag, they are all compostable, think of it that way, and the green waste will be composted or dug in. My understanding is that your kitchen caddy is for stuff which won't break down, stuff you'd want to keep away from rats and seagulls - meat, fish, sauces, cat food and the like.