Hello,
If it could help someone, Esri support answered about my problem which was this 400 error after applyEdits.
The (perfectible) solution was to limit to limit the maximum number of instance at 1 as parameter when the service is published. If you have more instances an applyEdits request will be sent to the AGS Server, and if the server is a bit overload, it will start a new instance. Your request will be processed by the new instance. Then, AGS will process that like if it's a new user (a different one) so it will lock the version while the other instance is working on edition. That was why I was unable to complete edition.
I'm not sure f it's really clear, but I hope it helps.
Ben