Switch App type from Private to Public

Once the app is created you cannot change that feature. The best you can do is to clone the app and make necessary modification in the clone app and then remove the original app

Yes, it applies for both public and private apps

The best option is to create a new app by selecting it as public and then give the required permissions to use that app

You can contact the RingCentral Support team through https://developers.ringcentral.com/support.html and submit a help ticket regarding the issue.

yes submit a ticket and just provide a reason for changing to "public" - I suppose you want to eventually publish to the App Gallery and the support team should be able to do it for you.