AnonMan: 1. What happens if you have a published client app (doesn't have to be Outlook). Users install it, but then later I delete the client app from Intune console (or unassign it from the users). Does the app get removed from their device or does it remain? Answer: For your specific scenario (removing the assignment), the app will remain. But different scenarios can result in different behaviors. If for example, you issue an MDM retire, the apps will be removed. If you change the assignment type to uninstall, the app would be removed.
2. What happens when you publish the Outlook app WITH an app configuration policy. Users install it, but Microsoft later release new configuration features which we then configure in the policy to company standards (e.g. 'Organize by thread' defaulting to off) . Would it change the setting for existing installations? Answer: an admin will be able to push the new settings without issue to existing managed Outlook app (however, keep in mind the conditions I outlined in the above article).
3. What happens when you publish Outlook WITHOUT an app configuration policy. Users install it. Focused Inbox is therefore on by default. You then apply a configuration policy with Focused Inbox defaulting to off. Would it change the setting for existing installations? Answer: Yes, it would get disabled (keep in mind the conditions I outlined in the above article).