How to apply a (in c# generated) normalmap right in Unity? (basic questions)

I am currently creating a new iteration of my procedural planet pipeline, and struggle a bit how to apply a by c# script generated normalmap right.

To make sure I do things right while searching for the bug, I have a bunch of basic questions how to use normalmaps in Unity3D.

a) When using a normalmap for a mesh, do I still have to apply the vertice normals to the mesh as well? Or will a normalmap "overrule" every information in Mesh.normals?

b) Am I right that a normal for a normalmap has to be applied always in tangent space, in difference to a vertice normal that is applied in worldspace?

What I mean, when I create a flat plane mesh that faces east (or x), a unmodified vertice normal would have to face in east direction (= Vector3(0,1,0) ) as well where for a normalmap the created vector stored in the texture has to face into z direction (= Vector3(0,0,1) because a normalmaps "up" direction is always in z-direction. So once the normalmap is then applied to the east-facing plane the normal vector would then be rotated to east direction according to the plane. Is that right?

Thanks a lot if you could clarify these points. I am afraid if the answer to question a) "yes even with a normalmap vertice normals are needed as well and they even depend on each other" then there might be more questions :-)

Thanks a lot everyone that can help me here!! Joerg