No it's more the case that Alzheimers and dementia are caused by other processes which reduce or end this process. And a lot of the damage isn't necessarily caused by reduce neurogenesis but by other factors.

I don't believe so, I believe there's a whole different subject matter on that. As far as I've read up on Alzheimer's, it appears to happen when too much stress is incurred on the mind or nervous system. That's just from what I've been reading on HackerNews though. There's stuff on beta Amyloid, caffeine, herpes... The list goes on but the decrease or nerogenesis doesn't appear to be related. I'm no expert.