Some questions to OAuth Consent Screen:
Is any data that I input while configuring OAuth Consent Screen editable? For example if I decide to change my app's name, can I edit that?
Yes you can edit the consent screen on google cloud console for the project. The app will need to be verified again if you change things like name, description, or any of the URLS like privacy and home page.
Does the OAuth Consent screen need to be submitted/verified/published in order to use it to test features like achievements or leaderboards?
Not sure on this one. My guess would be no if your just testing something it doesn't need to be verified until you are in production.
When choosing the support email, can I choose it from the list if I add that email to the project, or do I need to be logged in with that email and do the whole process from that account? oauth-2.0.
You need to create a google user with that email address. then you can add that user to your project and set them as the support email. They need to have access to the project you cant just add anyone.