Q. Can I run Windows Server 2016 and Windows 10 VMs on Windows Server 2012 R2 Hyper-V?
Microsoft has a strategy of N+1 OS version support for Hyper-V. For example, if running Windows Server 2012 Hyper-V, it is supported to run Windows Server 2012 R2 and Windows 8.1 inside VMs running on the host. For Windows Server 2012 R2, this will be carried forward enabling Windows Server 2016 and Windows 10 to be run inside VMs running on Windows Server 2012 R2.
Where possible, upgrade to the newest version of Hyper-V. The good news is, integration services are now delivered via Windows Update instead of through Hyper-V updates, so this makes upgrading easier.