Re: disease vs illness
Diseases usually last more long-term, yes. An illness does not have to be short-lived though. As you said, cancer is a disease. It is also an illness. I can't explain it any better than the others. We say "He died after a long illness". We do not say "He died after a long disease". If you plan to ask "Why?" every time native speakers say "That is just how we say it", then you are in for a long and ultimately frustrating battle.
Remember - correct capitalisation, punctuation and spacing make posts much easier to read.