M.P.
Sounds like his digestion is very efficient or not efficient enough. Does he eat a lot of fiber? Fiber does not get absorbed and instead passes our of the gut as poop after the nutrients are extracted. This is good! It's possible, I think but am not sure, that if his intestines are not absorbing nutrients his body will make more poop. I'd talk with his pediatrician and/or a pediatric nutritionist.
I suggest that he doesn't need to eat less banana. Bananas and dairy products can be constipating and he's not constipated. The BRAT diet is for diarrhea and he doesn't have diarrhea. If he does eat a lot of fiber you could try reducing the fiber but consuming fiber is really healthy and I wouldn't recommend eating less of it.
For the rash, I suggest smearing vaseline on his bottom after his skin has dried. I also suggest just using a damp washcloth. His skin may be sensitive to the chemicals in the wipes.
His waking up at 5 am may not be related to the bm. If he's actually aware of having a bm, then he might be ready for potty training. However, it's very rare that a 22 mos. old baby would be mature enough for bm training. Urine awareness comes first. Is his diaper soaked to the point of being uncomfortable? Do you use disposable diapers that pull the moisture away from his skin? Perhaps dealing with the wet diaper would allow him to sleep longer. Perhaps using a heavier or night time diaper would help.