Windows 2008 R2 — Generate new activation key for cloned machine

They are not required, but as you have quoted, they are recommended.

I have seen clusters where one half is a physical machine and the other is a VM.

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For support reasons in most cases you should not, but during a failover, as long as both sides of the cluster are able to handle the resource shift, you should be fine.

If all sides of the cluster have the necessary hardware, and resources, to handle a failover, it would be perfectly acceptable.

You can also run cluster validation to ensure everything will be fine.

You might want to make sure that the configuration you are running is supported though, since your server vendor and/or Microsoft might refuse support if it is not.

It appears that a Windows Server 2008 R2 Hyper-V Host can back itself and all its Hyper-V machines up right out of the box. The shadow copy service appears capable without any additional help.