Actually, I agree with all your terms, but diabetic. I think that is perfectly fine. I'm sure there is some grammer term for it, but I'm too stupid to know it. :P
While you won't find someone saying "I'm canceric", but rather "I have cancer", I think it's normal for me to say "I am diabetic" vs. "I have diabetes" (which is also fine to say.
It's the same as if you are sick. Do you say "I have a sickness" or "I'm sick"?
