You could use the Item Link for the group – select the group and use Copy Item Link from the Edit menu or the contextual menu. An option to copy the Item Link does not appear in the OS X Share menu, but when you copy it, the link is on the clipboard.
No. It is a DEVONthink-specific link.
If you need to share a folder (again, groups in DEVONthink do NOT exist): Have a folder in a shared / commonly accessible location and index it into your DEVONthink database. This is a common reason people will index folders in their Dropbox account.
Ah, you were thinking of “share” in the sense of “send it to someone”. I was thinking of “share” in the iOS / OSX sense of “send it to an app”. The link works in other apps, but not outside of your Mac.