Hi,
1. Does this compatible when Forest and Domain Functional level is increased from Windows 2008R2 to Windows 2016?
It should be compatible but Microsoft doesn't guarantee this compatibility .
I recommend to test the compatibility in your test environment.
2. Are there any issues observed when we remove all legacy DCs like Windows 2008R2,Windows 2012 and make the environment as completely Windows2016 Domain Controller based?
A DC on Windows 2012 or Windows has the same copy of NTDS database and sysvol folder, so it should be ok if you keep only DCs on Windows 2016.
3. Some issues are mentioned in below article but couldnt find anything related to Forest and Domain Functional Level.
Because Forest and domain functional impact only domain controller :by enabling new feature and define the supported OS version of domain controllers
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