How can I speed up dismissal animation of OS X notification dialog boxes?
You can dismiss all visible notifications by opening Notification Center and clearing notifications using the X at the top-right of the notification list.

Obviously this will remove all notifications for that particular date, so if you have others you want to save, this won't work. This is, however, the only way I am aware of to dismiss notifications en masse.

I'm also not aware of any way to remove the animations you mentioned.