Do I need to shut down each database individually when shutting my mac down? When I opened devon think pro most of my databases were missing . . .
You should not need to close your databases when doing a normal shutdown. OS X (e.g., Mountain Lion, Mavericks, Yosemite) should Quit each open application (Quitting DEVONthink will properly close open databases), and remember which apps were running at the time of shutdown so that when next started up, previously running apps are automatically opened with their previously open documents or databases.
Is the left Sidebar (View > Show Sidebar) of a DEVONthink view visible when you restart the computer and DEVONthink automatically launches? If so and OS X has behaved correctly, the list of Open Databases should include all that were previously open.
That’s what happens here, running DEVONthink Pro Office 2.8.1 under OS X 10.10.