Hey there- I'm going through a very similar thing. We found a baby mouse that was near frozen dead on our basement floor and I've been caring for him for several days, hes only about 2-3 weeks old. I've been feeding him KMR and baby food ever 4 hours. Hes having problems with solid food though. The little guy was being very tame til yesterday when it got much of its strength back and started to become a bit frightened of humans again, but is still letting us feed it.
If your mouse is nearly 3 weeks, he should be looking kind of like the one we have. You shouldn't need to help it potty anymore, but feel free to assist, its mother still would be.
4 weeks seems to be a pretty good age to wean them, according to everything I've read so far on the topic, but it can be different from mouse to mouse.
I don't have enough posts to post a link, but if you go to rmca.org >left hand column>Articles By Topic>breeding>caring for orphaned rats and mice there is some info on suggested weaning.
TheFunMouse.Com has tons of great advice as well, I'd recommend it.
As for if he might have diseases: I'm not a vet, but I would believe it is very possible. If there aren't any very obvious signs of disease, I would say your biggest problem might be mites due to the fact that he is already fluffy.