I mentioned in the other thread that dealt with running Hyper-V inside of a VMware VM, but since your asking about hypervisors in general for your HYV1 example, I will point out again that it is possible. Case in point:
Hyper-V running as a VM in ESXi running a nested VM
That screenshot I just took shows a VMware ESXi hypervisor as "HYV1", with a 2012 Server running Hyper-V as a VM inside of it (HYV2). That Hyper-V server is running it's own virtual machine (CL1) successfully.
Granted the performance is going to be sub-par and it takes some tweaking to get working, but it is possible for a lab setup. You basically need to trick Hyper-V to think it's not in a virtual machine itself. Whether or not this is possible at all in a nested Hyper-V in Hyper-V scenario, I do not know and would wager the answer is 'no'.
To your question about direct hardware access, can you be a little more specific? What type of direct hardware access are you trying to achieve? One of the key features of virtualization is a hardware abstraction layer, so the VMs (VMware or Hyper-V) don't really have direct access to the hardware but run through the hypervisor. You can pass some hardware through, such as a USB drive, to an underlying VM. I imagine this would work just fine in the ESX->HYV->VM scenario I outlined above, though I never personally tested it. You could also likely use RDMs to setup a similar access to hard drives. But I'm not sure exactly what you are trying to do.