Is it fair to say that Native windows containers for W2K16 will perform better than those based on Hyper-V?
Please see this presentation: Shows | Microsoft Learn
So, am I to assume that the Container being used in this case is a native windows container?
No, on Windows 10 only Hyper-V isolation is available. The Windows 10 kernel configuration is a little different from the Windows Server kernel configuration, so Hyper-V isolation is required.
Can anyone comment, or better still, point me at other sources of information that can clear up such confusion?
See above.
Also, does anyone know whether ASP-dot-.Net Core builds can be provisioned for Linux containers?
Would running Docker in W2K16 under Hyper-V be viable? Is that commonly done?
Yes, process (non-Hyper-V) isolated containers work great this way, and you can also use Hyper-V isolation if you enable nesting: What is Nested Virtualization for Hyper-V? | Microsoft Learn

