Rebels from Benghazi, Misrata, Zintan etc. all fought under the same banner.
Since when did you put so much stock in legal fictions? Do also note that there were rebels outside of the major coastal cities...

IS just opened a new front in Afghanistan (whether directly or indirectly). I am note sure what you are getting at.
What is the relevance here?

but unofficially, I can only assume that the most important leaders of the intervention had the goal to remove Gaddafi.
Unofficially, the goal was whatever you can imagine it to be.