In answer to your questions:
1. AppThemes does not officially support third party plugins, so unfortunately we cannot guarantee that such plugins will be compatible with our themes. In terms of this one specifically, I don't see any threads/discussion which indicates this is successfully bring used with ClassiPress.
2. The theme is not encrypted, so you can customize it as much as you want. You can read more about customizations
here.
3. & 4. Both would involve customizations on your part.
5. The theme has an advanced search functionality built in which allows you to specify custom fields which can be searched. By default this is visible only in the
category view sidebar.
6. You could potentially create a custom field relevant to the status?
7. We don't officially support customizations (or third party plugins), but support of the default product is available in the AppThemes forums. Thanks.