JobRoller doesn't include any private messaging options by default, however there are plugins such as
Envolve Chat which allow this kind of functionality. Plugins are installed onto the theme just like any other WordPress plugin, in the "Plugins" part of the WordPress admin dashboard (you don't see this in the AppThemes demo sites purely because of permissions, but it will be visible in a standard installation). To clarify though, AppThemes does not officially support third party plugins so we cannot guarantee that all such plugins will be compatible with our themes.
The job listing pages include an "Apply Online" link by default which allows job seekers to apply for jobs which is sent as an email to the employer. You would need to make some modifications to the default theme files if you were looking to remove this from the site as there are no settings for this in the JobRoller admin dashboard. Thanks.