In answer to your questions
1. The categories which are on the demo site are not populated in a new installation of the theme. You determine which categories are used for your site, so you can add whatever categories and child categories you like. This does not require customization and is easily configured from within the ClassiPress admin dashboard. The specific page for creating these can be found on the ClassiPress admin dashboard demo
here.
2. You can create a custom menu from within the WordPress admin dashboard as seen on the demo
here, so again no this does not require customization of the theme
3. There are two different layout options available in the ClassiPress admin, and that will allow you to either have the "Directory Style" (with the ad categories box on the homepage) or "Standard Style" (without the ad categories box on the homepage) layout. You can choose whether or not to display child categories, or whether or not you wish to display empty categories, or a specific number of child categories below the parent. These are all ClassiPress settings and do not require customization of the theme.
I hope this information helps. Thanks :)