Hi Cédric,
As an Administrator, you should be able to update the login name (looking from the account perspective, this is not the same as the email address, but of course you could add logic to keep them in sync) for other users. You cannot change your own username. For more information about the way access rights work using inheritance, take a look here.
It could be that certain restrictions are caused by the user management settings for the Admin role?
Hope this helps.