Ok, thank you.
My first suggestion would be a diet change as some dogs have sensitive stomach, something with Am Bullys are notorious for.
A good suggestion would be Hills I/D as this is suitable for all ages and sizes and is highly digestible and should help firm up stools.
The drinking is likely to make up for the water lost in the stool so is probably not concerning, but do keep an eye on this.
While he doesnt rush to eat, if he is growing well and is not under weight this wouldnt worry me.
While on a sensitivity diet, do not give any chews/treats/human food (which it sounds like you are already doing, which is great).
Do have a good check around the home and garden for anything that may be irritating his gut that he is licking/chewing such as grass, houseplant, cleaning products, carpet etc
If the issue persists, I would request a faecal analysis to check for e.g. a bacterial infection or resistant parasite, as well as a basic blood screen to ensure all is ok internally.