This is all with v8.2, with plan to migrate to 9 at a later date
Here's what we're looking into. To access one folder, users would need have AD authentication, for two other folders, user would need to authentication via Kentico's user management. The rest of the site would be wide open.
We also need to ensure any bookmarked URLs send the user to the correct authentication method, if applicable.
I'm digging further in to the documentation for this too.
Yes this can happen. You'd need to enable/setup Mixed Mode Authentication within Kentico.
Secondly, for ensuring proper access to specific nodes in your site, I'd default to whatever more pages need; either require authentication or not. So if the majority of your pages required authentication, then on the master page level in the Properties>Security, set Access to require authentication. This will then propagate through the rest of the site.
For each of the nodes which are "public" simply go to the parent node Properties>Security and set Access to not require authentication.