^You wouldn't get an apocalypse in a society engrained with the knowledge of what zombies are and how to deal with them, but yes, it would be a harsher society in some cases.
Correct. Think of it like Rabies: There would still be isolated outbreaks here and there. However, since people would know how to deal with them, casualties would be limited and the outbreaks would be quickly confined.
And I almost hate to bring up AIDS (both because of the political implications and because of Herschel's implications) but in our lifetimes we've seen how medical providers and first responders can adopt to a potential pandemic and people adjust to that: everyone now wears rubber gloves, there are special disposal methods for medical waste, condoms are more openly discussed, etc.
No doubt a post zombie world would be harsher but there is already precedence throughout history for people to adapt behaviors to pandemics without the world coming to an end.