Thanks to the flexibility of Linux, it's possible to run the OS directly from a USB drive, but is that the right approach? Here are the pros and cons.

If your external drive is not detected or recognized in Hyper-V virtual machine, you can follow the solutions and workarounds ...

It is the first thing you need to fix the issue as stated above. For that, you need to run the virtual machine showing the error and go to the Devices > Install Guest ...

Adding disk space to virtual machines is important to keep systems running properly and can be accomplished using Microsoft Server Hyper-V with either Hyper-V Manager or Failover Cluster Manager.