Role of Database Administrators
Of the tasks that you've listed the creation and maintenance of the user accounts in production should be done by the DBAs.  The developers shouldn't have the passwords of the production accounts at all.

Designing the tables, indexes and performance testing should all be done by the developer.  The DBA should be handling the creation of the objects on the production server, backups, etc.  The DBA will find any additional indexes which are needed after the system goes into production and create them in production.