No - they have very specific use-cases.
Shader nodes apply materials to geometry. Geometry nodes alter existing geometry or generate new geometry.
Doubt it - since they do different things.
In both cases Math is essential. To get the most out of GN it helps to know Vector math at a minimum.
No - a lot of users complain about how obtuse and difficult they are to work with. They are attracting people because you can do amazing things with it.
Hope that helped.