Can Qubes run inside a Proxmox VM?
No to nesting. I looked into nesting VMs once trying to recreate Qubes structure. Turns out nesting increases “attack surface” (which I think means adds unnecessary complexity). Xen with VMs is specially configured for certified bare metal. Are there better alternatives to Xen? Maybe. You think Proxmox might be? Even if so, then a whole other project needs to reconfigure things for you.
KVM as opposed to Virtual Box may have advantages in theory (although so much still needs worked out in practice).
Proxmox opposed to Xen may have advantages? Why do you think so? Again, in practice you have a lot to work out.
I don’t know about Proxmox, but it runs in VMware ESXi if you enable nested virtualization and nested IOMMU, I think Proxmox has similar options.
Seconded. Can be run “free as in beer”, installing Xen Orchestra from the sources and ignoring the subsequent warnings about “running from sources”. 
The result is a pro platform on par with VMWare.
yes it can be. i have done so before.