We took a pomeranian out of a bad situation and...?

I adopted a 3 year old Pomeranian from a bad home, the before morning we picked him up we were told he ran away. That evening he had a little blood in his stool the next day it was pure blood, today is is getting better. Since we just adopted him we don't know much about his history or how he usually acts. Hoping that this isn't a previously occurring problem and we got ourselves into trouble by getting him, what could the cause be? He's eating fine and drinking and no vomiting. We were also told he was potty trained, he doesn't seem to be though, is this possibly due to feeling sick? And again we were told he was neutered (recently) but he isn't acting like it with my moms female dog... Is that because it was recent possibly? .

We knew he was due for shots when we got him which is one reason I'm so concerned because if he is sick he is not protected with shots or a preventative.

The earliest vet appointment we could get is next week so I want some answers...