Adam,
I hope all is well. Great question. Hyper-V Live Migration Processor Compatibility is the same feature as VMware's EVC Mode.
What both of these technology features do is that they "blind" the VM to subtle changes in the instructions sets of the source and target host CPUs in order to ensure that the running VM will not experience a fatal failure while attempting to move between the two hosts in real time.
The main issues addressed are typically minor changes between family iterations of processors in areas such as multimedia instruction sets between different generations of the same family of chips, I.E., Intel SandyBridge Generation 3 vs. Generation 4.
To your scenarios then:
Server 2012 R2 to Server 2016 both using i7 processors, supported without processor compatibility enabled? It should be. BUT, the Hyper-V stack changes slightly between the Server 2012R2 and Server 2016, and as a result you always want to test to ensure there are no issues.
Server 16 to 16 both using XEON E7 processors, supported without processor compatibility enabled? Yes. BUT, remember as I suggested above, there is the potential for differences in chipset architecture and instruction sets even with a single family, as we move between generations, as a result, while it may work without having to set processor compatibility, it may also fail without it, depending on how close a match the two CPUs are (host source and host target).
Server 16 to 16 one using AMD and one using Intel, not supported? Nope. No way to do this on any platform, regardless of vendor.
Server 16 to 16 one using Intel i7 and one using XEON E7, not supported even with processor compatibility? Not necessarily, again, it comes down to the subtleties of the changes in the architecture and the chipset instructions between the platforms. It would most probably fail, but I have had strange results in situations like this one with both VMware and Hyper-V in the real world. The best path here is to enable it and see if it does or does not work, as that is the only way to know for sure.
Having said that, for exam purposes, the answer should be NO.
Hope that helps :)
Cheers,
The other Adam