Any bread you buy is supposed to be consumed within 3 days of manufacturing. You keeping the bread in the fridge is not going to extend its shelf life. In fact, when you keep the bread in fridge it dries up and becomes stiff, and might turn inedible even before its expiry.
Bananas hail from tropical climates and they have no defence mechanism against the cold. So when you stick them into the fridge you are actually making them rot. If bananas are green and you put them in the fridge, they won’t ripe at all since the enzymes require warm temperatures to work.