Please familiarise yourself with this page:
http://docs.wpgeodirectory.com/layout/
You cannot edit a file for a particular category page, but if you are OK with coding you can change the template that is used for all CTP and category pages.
Some widgets adapt to the page, meaning that if you change from hotel to restaurants, hotels will no longer be listed but restaurants will.
Other widgets do not adapt, like login widget for example.
The sliding widget indeed does not adapt to the page. Maybe this is a request that can be made, ie to add a [location] filter to the widget like the Popular Post widget for example. Look in the right sidebar as to how to make requests.
There is currently no way to remove the country from the breadcrumbs.
Clicking on that big ‘delete dummy data’ button will only delete the sample/dummy listings.
The “GD Home page” template is NOT only for the homepage, it is also the template for all locations, see http://docs.wpgeodirectory.com/layout/#home
But you can add widgets that adapt as explained above, and you can add specific widgets like the “GD Location Description widget” which will change content if you change settings at GD > MultiLocations > SEO Settings
Example: http://goldroo.net/directory/australia/queensland/brisbane/ (Look in the right sidebar).