Is there a action-window phase before the first conflit and after each conflict ?

There is an action window before each conflict opportunity. (pg.30 Conflict Phase) so you can reference the full wording of it.

Yes.

https://images-cdn.fantasyflightgames.com/filer_public/b3/b7/b3b74cee-5ea1-44f7-a459-466c3d7edc81/l5c01-rules_reference-v101.pdf

Pages 18-19 have a great easy-to-follow chart of the phases with all the action windows marked.

I found that chart a little confusing until we worked out a specific detail that made it clear in my head. There is an action window between 3.1 and 3.2 where 3.2 is when Conflicts are declared *including* the first conflict of each round. After each conflict, go to 3.1 -> Action Window -> 3.2 Declare next conflict

Start the phase with an action window and end the phase with an action window, alternating Action Window - Conflict. Easy way to keep track.