Yes, both can drink the probiotic water. Probios are good for all life, we all need good bacteria in our digestive tracts.
Never think you are being paranoid when it comes to your birds! You know them better than anyone else and those that watch this carefully as you are, are good keepers.
At her age, she shouldn't have wet poop so something is going on. When I have sick birds, I try what ever I can so I can rule out things, worms and cocci are common and why not rule them out! Of course we can't change genetics or some organ issue she may have started life with. I don't think you should jump to antibiotics just yet, that is why I am suggesting the natural things that might aid her healing. If these things don't work, you might try some amoxicillin on her. If nothing works on her, you might try and find an avian vet that knows birds.
Is she laying yet? Coturnix quail?