I'm sorry you feel that way matey. I'll try and help you best I can, I'm even happy to have a quick look in your admin setup to see what's happening. I've tested what you've described on my Lite version of Classifieds, and I can get the categories access to work correctly.
I'm assuming that there is some minor detail we're missing that is causing the issue.
First, if you've reinstalled then there won't be any categories in place. You'll need to add some (if you've not done that already).
The main set of usergroup permissions are the ones you included in the images above in the Usergroup Manager. They deal with just the usergroup's
general access to Classifieds.
In the Categories Manager in the Admin Control Panel you can tick which usergroups you want to have permission to see and access those categories. So for each category if there are none ticked, then
every usergroup can see them.
If you tick certain usergroups in a category, then only those usergroups can access the category. So if you've checked Administrators and Moderators, then someone in the Registered User's wouldn't be able to access the category, and that includes any existing listings with that category selected.
It is possible that if a listing has lost it's original category, then access might be restricted. I'll check the code this week to make sure there is a work around if that should happen (all though I imagine it unlikely, but you never know

).
Does that help at all?
If you do want me to take a look for you, feel free to PM some Admin access details so I can check it for you.