I'm not sure what you're looking to accomplish, but it sounds like a mix of wanting a realtime OS, CPU shielding/affinity and a standard Linux or Windows userspace for development; all on standard hardware.
That gets you a realtime kernel and OS. If you need to run specific tasks on a specific CPU or CPUs, you can use CPU shielding techniques to perhaps, create a group of CPUs for the OS and another group reserved for your realtime application execution.
Usually realtime and virtualization don't go hand-in-hand. The operating systems listed above provide extremely granular control over processes, scheduling, priority and interrupt handling.
I suppose that depends on what you want.
If what you need is a real-time OS to run some DAQ and/or control software, then yes, Linux with the RT patchset offers the usual real-time OS features.
If you want an alternative hypervisor for running Labview RT, then I don't know. It wouldn't surprise we if it refused to run on anything but their own hypervisor.
you mean like Hyper-v. I don't see from the link that the hypervisor your link to does anything special that every type 1 hypervisor doesn't do.
Update - after reviewing it further it appears it contains support for some specialized hardware : "In addition, the Real-Time Hypervisor is specially designed to maintain the determinism of LabVIEW Real-Time programs"
VxWorks and LynuxWorks both have hypervisors based on hard-realtime schedulers, certified to go airplanes and such. They're NOT cheap, but they do their job.