1. I believe Yammer is soon enabling the ability to have users automatically added to a group based on their Azure AD record. That functionality does not exist yet, but I believe it is on the roadmap for this year.
2. Not sure how large your organization is, but any group in your network should be able to welcome all network members.
3. This can be done as long as it is a private group.
4. This may be able to be done in Sharepoint/O365 permissions, but I am not optimistic.