For completely private boards where only registered users can see content and registrations are turned off:

The create account button be hidden if board registrations have been turned off.

There should be an option to selectively have the board only display the login screen for anyone who is not logged in, hiding everything else. (Ideally this would have bunch of checkboxes for all the home page areas, so you could selectively disable/enable them.)

This is already setup this way in permissions. You can set the guest permissions to where they get a page very similar to a closed board, where you can add content explaining something like this… This is a members only forum and with our due regret we are not accepting new members at this time.