My GPs adored banana, but I think nana skins have a lot of fungicide residue, so for that reason alone, skin off. Melons are fine as far as I remember (just googled and that said they are ok, too). But may not be too nutritious, so not to overdo.
I love GPs, you can feed them all the veg peelings, fruit waste, etc, just about anything except not rhubarb nor celery. As long as they have enough hay and a source of Vit. C, they're pretty easy.
I give ours the bits dd doesn't eat. She never eats down to the core of apple for instant, or right to the stone of any fruit, or to the skin of the melon etc so they get all of that and clean skins and stones thoroughly. Stones get played with. I've not tried mine on banana.
Overdose of vitamin C will give anyone the runs, so if you're giving them stuff with lots in (fruit as opposed to veg) just give them less. Though citrus fruit is to be avoided.
I was warned off tomatoes - apparently they are very acidic and burn their mouths. Perhaps my 2 are sensible gps as I had given them tomatoes before I found out I shouldn't, and they wouldn't touch them!
Celery ok as long as sliced, it's the long fibres gps may struggle with. Parts of potatoes you would eat are ok, too -- it's green potatoes, leaves, root eyes that are poisonous to them (as they are to us). I think rhubarb is entirely bad for them, though. Iceberg lettuce just isn't very nutritious, full stop!
Ours adore melon and celery. Also cucumber and avocado, peppers- we don't peel them tho Fio... I didn't know that about babnana skins Peanut- we've been giving them to them for years and they seem ok... They seem to really appreciate variety, and get excited at the prospect of different meals! And each one has their favourite things....