I have seen my rooster eat a banana. Our chickens love to fight over black bananas.
They also got half a watermelon yesterday b/c it sat in our fridge too long, and they routinely get apple and pear cores. So far, the only things I won't throw them from our table are very fatty meat or things with lots of garlic and onions in them (because of egg taste). Pullets get things with garlic and onions in them like leftover chili since they aren't laying yet. So far, they'll eat anything but let raw carrots sit a while. We don't have much of a compost pile any more.
I haven't seen any difference between when when they get lots of fruit (high garden season, they get any wormy veggies or fruits) and when they get just a little (spring and later fall). Weather seems to play the only large role in how well they lay. We do supplement with cat food in winter when they aren't out eating bugs.
Where have people heard that bananas aren't fruits? They are the fruit of the banana plant and fit the definition of "fruit" perfectly. From Webster:
Fruit: b (1) : the usually edible reproductive body of a seed plant; especially : one having a sweet pulp associated with the seed
Banana:
1 : an elongated usually tapering tropical fruit with soft pulpy flesh enclosed in a soft usually yellow rind
2 : any of several widely cultivated perennial herbs (genus Musa of the family Musaceae, the banana family) bearing bananas in compact pendent bunches
They could also be called berries, I suppose, but not for any special reason:
Berry:
1 a : a pulpy and usually edible fruit (as a strawberry, raspberry, or checkerberry) of small size irrespective of its structure b : a simple fruit (as a grape, blueberry, tomato, or cucumber) with a pulpy or fleshy pericarp c : the dry seed of some plants (as wheat)
