Ageing is not infectious, so it doesn't make sense for it to be on a list of infectious diseases.
As fun as it sounds, I think aging is what drives humans to progress and evolve. So just in my opinion, I don't think classifying aging as disease is a good idea.
Are we still evolving, since we usually die much after breeding ?
Yes.
How?
We're currently selecting against drug addicts. It might take a few dozen generations to notice the effect
Reducing aging wouldn’t have any effect on that, though?