So I start with a normal cube > I Extrude and it doesn't work right ( Grey faces and missing faces ) I try to move a face/vertices with G and right click but it selects some sort of ghost vertices. Help I can't solve this and it's making me want to give up Blender. I tried looking for solutions but it seems like it's a bug.
It doesn't look like a bug to me. There are 3 types of selection modes in blender; Vertex, Edge and Face. You have to select them according to your requirements. If you select any of them and press 'E' to extrude, it extrudes along the normals by default. If you want, you can constrain your extrusion to a specific axis by pressing 'E' to extrude and then X, Y or Z for x, y and z axis respectively.
The second problem you mentioned is shading problem according to me. After you've finished your extrusion and modelling, select the whole mesh in edit mode by pressing 'A' key and then recalculate the normals.