We have also seen some inconsistencies re. sharing of folders/documents not with groups but with all attached to our domain. Have you tried sending the group a link to the parent folder? When the link is clicked on it may then make that folder and its children visible to the group under "Folders Shared with Me".

In the New Google docs editor, the Google Analytics built-in tracking and the insertion of custom HTML code were removed but they could be extended through add-ons and Google Apps Script.

Some methods and triggers are only available in bound scripts. You could use Google Scripts, the editor to hold stand-alone scripts, to create web apps and to hold code libraries that you could call from bound scripts.

References

Extend Google Docs, Sheets, and Forms with Apps Script