Hi Tiffany,
To answer your first question, the Outlok plugin does pull the activity type "work order" (if you go to Outlook Add-in Settings, and go to the Appointments tab, you will see all the activity types in the "Synchronizethe following activity types:" drop down).
To answer your second question, it is possible to sync Google Calendar with outlook using Google Sync, which as per the above, syncs with Field Services. So provided you have set these up correctly, you should be able to sync Google Sync with Field Services through Outlook with the Outlook Plug-in.
Hope this helps,
Denis