Does Growl logs all the notifications that it handles? And if yes, is it possible to view a list with all of them?
It's not a built-in feature so you won't be able to view past logs. However, you used to be able to enable/disable logging of notifications with scripts I've included below but I don't know if these still work. If they do, then you could enable logging of future notifications.
Enable Growl Notification Logging:
Disable Growl Notification Logging: