CB Privacy tabs

I read the doc and watched the video tutorials too. I hope I'm just missing something.

I picked "user can control privacy" for Group tab and Connections tab, default Public. Seems to work fine for profile visitors.
But, the user sees these extra tabs "Groups" and "Connections" when they edit their profiles. Each tab just shows the connection types dropdown menu ( the ones enabled) and nothing else.

Not obvious at all to the user what is going on there. Can I change how it's displayed? Can I add text? Can I put the privacy selects under a single "Set Privacy" tab? Better yet, can I just pretend it's another field setting in the normal profile tab?

Can I change how it's displayed? Can I add text?

Yes, but it will require making a custom template for CB Privacy to change how things display.

Can I put the privacy selects under a single "Set Privacy" tab?

Yes, you can enable the simple privacy mode as shown the below blog post.

www.joomlapolis.com/blog/kyle/18860-cb-privacy-6-1-0

Better yet, can I just pretend it's another field setting in the normal profile tab?

Yes, you can use a Privacy field to move the privacy controls to a separate field that you can move around. The asset for the privacy field should be set to "profile.tab.TAB_ID_HERE" for it to control the privacy of that tab. Then for the privacy controls on the tab set its Layout to Hidden so it won't actually display. This is a more advanced usage though and recommend using the Simple privacy mode as it's most clear for users.

The Simple Privacy mode works fine but now I would like to add another custom field (radio button type) to the Privacy tab. I see right now that only fields of type "Privacy" go into the simple mode Privacy tab. How do I get the radio button type field to go into that tab?

Maybe you have a better approach. I'm using this field for a particular usergroup to be able to hide themselves from user lists ( while their profile is still accessible).

The simple privacy tab is strictly for privacy controls only. You cannot add other fields there. You'll need to place your field on a different tab. Removing users from userlist only works with the profile privacy field check so it's not possible to replace that with a different privacy selector only for userlists. That maybe something supported in the future though.