Is my external USB drive causing erratic sleep/hibernate behaviour?
To determine the sleep mode it is using, you would have to peruse the system.log in the Console.app (Applications > Utilities).

The problem when trying to wake it up sounds like there is an issue with the external USB drive not responding properly.  It could be a compatibility issue with the drive, the "USB mini-hub" is getting in the way, or a power-related issue where the USB hub needs power from the Mac to spin up the USB drive but it can't until the Mac responds.

Try plugging the drive directly into the MacMini instead of using the USB hub and see if the problem continues.

You could reconfigure the power management settings to not sleep.  The MacMini uses very few watts of power when idle so the cost is minor compared to the issues here.

You could also try using this command to configure the USB drive to not power down when idle.  This might trick the MacMini into thinking it is still being used so it wouldn't go to sleep.  (It has been a long time since I used this command so I'm not sure it still works)

/usr/bin/touch /Volumes/USB_DRIVE_NAME/.keepDriveAwake