If I restrict internet usage, will the app still be able to function properly and update?

It depends on the App developer, if they require their trackers to connect to their servers prior to the content being displayed. For apps that don't require internet access, we suggest that you turn this off. 

If the app does not function properly, then look at their permissions, and the network connections behind the app. You can do this inside the Redmorph app. Based on this, you can decide if you want to provide internet access, and then determine the protection level just for that app.

You can allow the app to make connections with its direct URLs, but block other analytics and 3rd parties in the live view.