Oh yes, he's cute alright.
As long as he has a ready supply of fresh water then the chances are, he'll drink when he's ready. You could try moving his water away from the food dishes, as sometimes cats prefer their water to be sited elsewhere. You could also let him explore a gently running tap, under supervision, to see if he likes that.
I know we hardly ever see Tinks or Moray drink (and when we do its inevitably out of the pond, and not the wonderful cat fountain we bought them
) Has the tummy situation calmed down? You can check to see if he's dehydrated by pinching the skin gently at the scruff of his neck and looking to see how quickly or slowly it subsides. If they're dehydrated, skin takes longer to return to normal. It's possible if he has an upset tum that he needs some water, but the cat milk suggestion is a good one, and if his poo problem has eased, I would just keep an eye on the situation to make sure it doesnt recur.
It's easy to forget that whilst we're having so much fun watching our new cat and existing cat interact, it's an enormous change for new cat - change of home, change of food, change of care-giver, change of cat companions. As kittens they tend to take much of it in their stride with the right encouragement, and I think you're very good at keeping an eye on things and offering that encouragement, so keep up the good work.
Bebe's such a lovely cat, isn't she? She seems to be taking Bruno very much as she finds him, and is interested in him, as a new companion.