I'm rating this 5/5 because it's awesome and mandatory these days.
Q1. Is it possible to add an option to hide the toolbar icon (and any other UI reference to this extension) if "Disable Private Bookmarks outside of private browsing" is enabled?
Q2. Or maybe it is possible to show the icon on the toolbar only in private window?
Unfortunately Firefox does not allow extensions to do this. What you could do is remove the button yourself through the right click -> customize menu and access the extension through keyboard shortcuts. By default this is Alt+Shift+8.
