I'd like to authorize the responsible of an activities to assign ressource to his activity even if he is not the project leader. is that possible?
Moreover, i'd like that the responsible of the activity could update the "rest" case in his activity.

All of this is managed through specific access right.
So you can define some profile that will have member access to activities with additional right to uptade assignments.
But this cannot be managerd for "responsible" only.
Only full access to activity can be restricted to "responsibe"