1) Can the Impact Metrics data be downloaded?
If your instance is connected to the Cloud Analytic's service (Requesting access to Jive Cloud Analytics) you will have access to the DES (Using the V2 Jive Data Export Service (Analytics)) service, which would allow you to obtain this type of information via API calls. However, there is not an option through the UI for this type of information.
2) I'm on version 7.0.1 with mobile friendly turned on. Is there any way to get the categories created for a group to show on this view? (currently it only shows recent content/activity)
For clarification, are you using an app to access your instance, or are you accessing through your mobile device's native browser? Or, for clarification, can you provide a screenshot of what your view looks like.
3) Is there any way for a group admin to auto-approve requests to join? Or is there an easier process than having to log in to the site?
There is not an auto-approve option for private/secret groups, however, if you are wanting users to automatically be added to a group I would suggest using an open/members only group.