1. Yes, you can add additional pages to the navigation menu, simply by creating a new page within the
wp-admin dashboard.
2 & 3. Could be achieved with some custom coding on your part, but they are not standard settings you can change in the ClassiPress admin dashboard.
4. Yes, you can choose not to use category icons, they are not there by default.
5. There is already a search feature in ClassiPress that allows you to search for key words. There will be improvements to the search in a future release of ClassiPress, however if you had your own advanced search in mind there is no reason why you cannot customize the theme to suit your needs yourself.
6. This is not a standard feature of ClassiPress. Again, would take customization on your part.
7. There is not currently a feedback system in place in ClassiPress.
8. The out of the box theme only allows for image files to be uploaded, so any other formats would be a customization.
9 & 10. Again, customizations of the theme which can be done by someone with enough coding knowledge.
11. There could be a plugin which allows you to compile your list of users, otherwise again this would be a customization of the standard theme.