Role of long-term asymmetric keys in a forward secrecy instant messaging protocol?
I don't think you are wrong on any of the points.

"Perfect forward secrecy" is a confusing name. Indeed it means that somebody who gets hold of one of the keys cannot use it to decrypt messages from the past.

There are two more properties you usually want:


When somebody does impersonate Alice or Bob as you suggest this should cut the real partner out of the conversation to make it detectable.
When somebody acquires a key he should not be able to decrypt messages after Alice and Bob have switched to a new key. Sometimes called backward secrecy. 


There are probably more that I didn't think of right now and it case of group messaging it becomes even more complicated.
Dealing with these will make your steps (3.) - (5.) much more complex!