Yes exactly when you remove a piece of the build system the build system stops working.
When I use bazel I need python installed or it doesn't work. That doesn't mean my build system is python. It means my build system takes advantage of python. Same for cmake and make.
Yes. Make is a build system. Cmake is also a build system that leverages make. This means that from the perspective of a user of cmake, make is a component/dependency/part of cmake. make can be used independently, and is absolutely developed independently, of cmake.
But when you remove a dependency of a tool you can expect the tool to stop working. That doesn't mean that the tool doesn't do what it says it does.
no, you don't
remove from your system make (ninja, msbuild, ...) and see how cmake builds your project