Is my pool's gunnite showing through?

I guess I don't really know the makeup of my pool surface. I have
some areas where the plaster has flaked off. The thickness of the
flaked plaster is about the thickness of about 6 sheets of paper.
Underneath, there is also a white material that is kind of rough. Is
that plaster also? Can I patch these flaked areas and if so, with
what material and what steps. Also, is it possible to paint the
inside of a pool or will the paint just flake off?

Thanks, Chris

.