where can I find the sent items from Microsoft Outlook for Mac in an backup image and how do I get them imported?

Depends on what version of Outlook you're using. The item you want to find is as follows. In both cases, the last item is a folder that contains everything related to Outlook. Emails, accounts, contacts, etc.

Office 2011 or earlier:

/Users/account_name/Documents/Microsoft User Data/Office 2011 Identities/Main Identity

Substitute 2011 in the path name accordingly for Office 2008

Office 2016:

/Users/account_name/Library/Group Containers/UBF8T346G9.Office

By default, the Library folder of each user account is hidden. There are a couple of different ways to get there. One way is to be anywhere on the desktop so that the name of the foreground app in upper left by the Apple logo says Finder. Then press Command+Shift+U. This will open the user account folder of the person who is currently logged in. Now press Command+J. There should be a check box on the bottom to make the Library folder visible. Check that box and close the View Options panel. Now you should be able to see the Library folder in your account and can navigate to Group Containers. The current UBF8T346G9.Office folder should be within that.

This is all presuming booting to macOS, but it sounds like you can't do that yet. Or, have you already reinstalled macOS and just want to get at your backed up Outlook data? The above would make the Library folder visible after a reinstall, but I'm guessing the Outlook data folder won't be there. I personally don't use Time Machine, so couldn't tell you how to proceed retrieving it from there. But another guess would be the disk image you saved off the non bootable macOS drive is the one you want, since that would contain the most current emails. Yes?

Why are you using parallels in addition to bootcamp? Not sure where to find the file but that could be part of the issue with OS X not booting at least.

Sorry, wrong key combo. It's Command+Shift+H.