if VMWare Fusion provides the Virtualization features to the guest, then yes. If not, no.

But then again, that is true for all VM-nested software.

Probably, if you enable nested virtualisation it runs most things, eg nested hyper-v, nested xhyve.

typically not, once you use a virtualisation instruction on the CPU it cannot be passed to the guests.

Nested virtualisation typically uses emulation without hardware acceleration.

I don't see why you couldn't parse the virtualisation instruction to a virtual machine. Modern hyper-visors don't emulate the CPU instructions any more, they're parsed through to the virtual machine.

While I'm certainly not sure, I do believe that at least some virtualisation solutions are able to parse the virtualisation instructions from the host CPU to the guest.

You only need to emulate the virtualization instructions. KVM does this and pretty much everyone else does too.

Hyper-V runs under Fusion, Qubes OS and Xen also work. Have not tested others, but this is one area where Fusion excels. Yes it will be slower, but for testing the concept that is usually fine.

I needed Xen for some experimentation. I had trouble running alpine-xen-3.4.4 in Fusion. XenServer 7 seems to work in Fusion, but I don't like it. I finally managed to get alpine-xen running inside KVM (Ubuntu 16.04) inside Fusion.