Awwww poor baby!!! *sends her healing strength and love to Mittens*
I will definitely be sending him some energy.
I dealt with a sick kitten about a year ago when the outside kitty (she's a stray) I would feed, got pregnant. She only had 1 kitten and it didn't do so well.
I feel bad because I think I intervened too much and I basically moved the kitten from where she was nursing it to a safer spot. She had it next to a cactus in a bed of ants kind of out in the open for birds to get it and stuff. I moved it to under the awning of our building and put out towels and a box and stuff. I left for a short bit and when I got back the kitten was gone and the stray kitty was back at my doorstep meowing.
I have a lot of guilt about that still.
Yes, kittens can have diarrhea for various reasons. It's not normal per se but can be remedied. I used to work in vet clinics and we saw it often. Typically, it's b/c they either have parasites (worms or giardia - an intestinal parasite), have too rich of a diet, or their system is just so out of whack it's basically not functioning correctly. Mitten's probably needs fluids, you can shoot water down it's throat with a syringe (no needle) or if he'll drink get him to as much as he can take. Otherwise, I would recommend taking him to the dr so they can hook him up to an IV. You should also feed him either chicken or turkey (no red meat or fish right now) wet food mixed with a few drops of water and you might even warm it up in the microwave a bit b/c that makes it more pungent and cats like pungent things.
I have to stay it doesn't sound good. I would take him in for the IV but if it's too costly or you just don't want to risk moving him. Try getting liquids and a little soft food into him. Also kittens need to be warmer than we realize. Cats run about 101-103 degrees normally. If he's just resting, you might make a homemade warm pack by sticking a paper towel or washcloth in a zip lock baggy and zapping it in the microwave for about 20 seconds (make sure it's not scalding hot or burns you 'cause it'll burn him) then just gently rest this beside him.
I hope this helps! I'm sending Mittens tons of love and strength. <3