You are correct on that setting. I had it set to registered. I guess even is its set to Public a non registered user is not able to see profiles unless they are registered. Is that a correct assumption?

Correct.

If I leave Profile View Access Level to registered and enable the Privacy "Public" rule then than basically means Public to all other users only. Does that make sense?

Yes.

If I set Profile View Access Level to Public, then I should keep the Public rule disabled and make the User Rule set to Registered? Could this work to?

Yes.

So, I understand better. Do these settings in the images below amount to the same thing in that "Users" and "Public" mean when users select this privacy option is only means registered users?

Yes.

To further complicate the scenario, if I wanted view access to only be a specific registered user group only (in other works if it's set to users [or public], what setting should I be looking at?

Enable the privacy rules for usergroups on that same exact tab you enabled Public and Users. If you mean you only want that privacy rule available for a specific view access level then adjust the access parameter under that privacy rule in the privacy rules settings.

In my case, I just wanted the paid users to know that when they select "Public" or "Users" it only means users in the paid usergroup, not the free users who are placed in a different usergroup. So then what you suggest, setting the usergroup group to the paid usergroups would accomplish this?

No, that parameter controls who can select that privacy rule. Sounds like you just need to translate Public to Users since you don't have publicly accessibly profiles.

2. If I am using Public to mean users, is there any need to enable the user rule? Does it matter either way?

Just translate the Public user rule name to Users in that case and turn off Users privacy rule. Each of the rules use a CB Privacy specific language key so they can be translated easily using language overrides. For Public its language key is PRIVACY_PUBLIC.

3. If I set the Public or User access to the paid usergroup rather than registered, does that only mean that group can select those options in the privacy settings? (sorry if I am repeating myself - I want to make sure I get this right)

Yes.

What I wanted to make sure of is that The Paid Users, when they select either "User" or "Public" in the privacy settings means only other Paid Users have access to their content. In other words, "Public" or "User" also excludes even the Free Plan Usergroup.

That's not what Public or User does. Use the usergroup privacy rules for that where they will be able to select the "Paid Plan" usergroup specifically.

Public = Everyone
Users = All Registered Users

If public profiles are not enabled then the following is true.

Public = All Registered Users

I have managed to prevent Free Users from seeing anyone else's profile (even other free users) by simply setting "Profile View Access Level" to the "Paid Plan" Usersgroup (Which then means, I can used the Public Rule)

This will cause problems with users being unable to access themselves in some cases. Usually all ajax endpoints break by locking a user out of their own profile. I don't recommend doing this.

1. Is that sufficient to protect the privacy of paid members among themselves or is there another rule to consider?

I suggest using the following.

CB > Configuration > User Profile
Profile View Access Level: Registered

CB Privacy > Privacy > Rules
Public: Enabled
Users: Disabled
Usergroup: Enabled
Usergroups: Paid Plan Usergroup

Now they can choose for something to display to all registered users or just to those with a paid subscription or you can choose this for them using forced privacy controls. Now for example you can make a tab only visible to a users self or if they're a subscriber using the below.

Integrations > CB Privacy
Display: Forced privacy control
Default: Paid Plan Usergroup

You can't currently do this for the Profile Privacy field though since it needs to be visible on profile edit or registration for it to check those privacy rules, but have added a feature ticket to support forced privacy controls for it.