That helps a lot thank you ! 
It is pretty clear now ! I tried to export one of my cloth sim and it worked well. I’ll stick with it to import my character’s action in other scenes.
In your reply you also wrote about the “Bake all dynamics” button, but in my project this button only bake 1 of the 5 cloth simulation, the 4 last have a “0 frame on disk : cache is outdated !” on their properties panel. Deleting bake of one of them doesnt reset the cache, and then hit “Bake” only goes through the frames without any calculation, any idea on this ? Thats weird.
In any case, thanks for your help, this is a solved post !
I’ve also made a post a few days ago about my cache issue, if you wanna save me two times in a week haha : 0 frames on disk, cache is outdated : unable to reset multiple cloth physics cache
Thanks again for your time, bye ! 