I think KubeVirt fits better in an environment that is already running Kubernetes. We have found it useful for running some of our heavyweight CI jobs that have virtualization requirements because we can manage the VMs in the same way that we manage our containers.

In general though we have only used KubeVirt for ephemeral workloads.

See: "Comparing KubeVirt to other technologies":

https://kubevirt.io/2017/technology-comparison.html

In the end you need an infrastructure where you run your kubernetes cluster on. Haven't used it yet but how I understand it, it jut provides you the kubernetes experience to provision VMs. It seems like the VMs are actually running in a container which in the end runs on a kubernetes node.

yes it can, see the "demo" os from the rancher guys:

https://github.com/harvester/harvester

they created a flull blown virtualization stack with a gui.