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Based on what you have written about Casey, I am quite concerned. First with regard to the dark, black stool, this indicates internal bleeding in the upper part of the digestive tract. The dark color comes from digested blood. Usually with this sign there is an ulceration, but in some cases a dog can have a bleeding problem or other issue causing the internal bleeding. This warrants a visit to see his vet ASAP! The second issue is the rash you have noticed. Is this rash itchy or does it look like bruising? This may be an unrelated skin infection OR it could be an external sign of a bleeding problem.
It looks itchy because he licks it.
Then, this is probably a good thing with regard to the rash. It is likely unrelated to his vomit/diarrhea. With regard to the vomit/diarrhea could he have gotten into any rat poison, eaten/destroyed a toy or other foreign object that could be in his system? Are you noticing any yellow coloration to his skin (this is easiest to see in the whites of the eyes)? Also, if you lift up his lips and look at his gums, are they a normal pink or are you seeing any of these issues: white/pale (in comparison to tongue color), yellow or spots (small or large)?
I am focusing on the vomit/diarrhea because BLACK stool can be a life-threatening issue.
Let me know if you have further questions. It looks like you exited the chat. My absolute best recommendation is take him to be seen by his regular veterinarian right away.
Best of luck,