Where would I find if a task is running and/or proxy generation is happening?
It is in the Tasks pane at the bottom left area of your Contact Sheet window (you currently have it hidden). You can make it visible by clicking on the horizontal splitter and dragging it upwards.
Do I need to resync the offline HD now that I've unplugged it to test it?
An offline drive cannot be synced. It must be online during the sync and the proxy generation phase. If you've been unmounting it before these tasks complete, that would explain why some of your proxies are missing.
Make the Tasks pane visible and see what's going on.
-Kirk