How to show category and subcategories on category page

I have custom post type for classified ads.
In that I have categories like cars, spares, accessories etc.
In cars I have sub-categories like alfa romeo, honda, toyota etc.
For each of these sub categories I have car models as sub sub categories.

Now when someone clicks cars category from home page … I want to show a page that lists Sub-categories and sub-sub categories. I can see the sub-categories in the sidebar due to a widget but do not know how to show them on the main page.

Also, is there a way where I can have a dropdown for category and sub-category (auto populated as per category selected) and sub sub category dropdown (again auto populated as per sub category selected). This I would like to be in the sidebar.