Groups, by default, do not show the email addresses to any roles other than Owner. To make addresses visible to Managers as well:

1. In My Groups, find your group and click on Manage to view the Group settings.
2. On the left side, expand Permissions and click on Access Permissions.
3. Find View Email Addresses.
4. Expand that drop-down list and click on Managers of the group.
5. Click Save.

Yes, groups can be nested. This can save the group managers time. If you need to add or remove a member from multiple groups, you just edit the smaller group to which the member belongs. All of the larger groups are updated automatically:
https://support.google.com/a/answer/167100?hl=en

A Google Group may not however be a manager of another group:
https://support.google.com/a/answer/167094?hl=en

This is a known bug in Groups that Google engineers are working to fix. They will let us know once it is fixed.

No, there is no template function for the Welcome message at this time. The easiest workaround is to copy-paste text from a file into the Welcome message field.

There is currently no method for bulk deletion of selected members.