Is there any caching implemented on Region / Include Page URLs level? If yes how to validate it's being cached? As I am using Include Page URLs for shared layout components such as header and footer and I want to make sure won't result in any performance issues.
DXA 2.x uses a Model Service or (for Sites 9.0 and higher) a DXA Model Extension for the Content Service. In both cases, Include Page expansion is done in the DXA Model Service/Extension and it is leveraging CD Caching for the purpose.
So, yes, DXA Include Pages should be heavily cached in the DXA Model Service/Extension. On top of that, DXA caches the resulting Page Models (containing Region Models for the expanded Include Pages) in the DXA Web Application (less aggressively, using time-based caching).
It still makes sense to do some performance tests on your DXA Web Application to ensure it meets your performance requirements, of course.