Well you create a mesh, but you don't point it to a mesh in your scene. When i have loaded an .fbx file i create a mesh pointer and then go into my scene and grab the mesh. Consider this code.
FbxMesh* mesh;
FbxNode* node = myScene->GetRootNode()->GetChild(0);
//I want my mesh to be formed by triangles so i convert the mesh into triangles
FbxGeometryConverter lConverter(node->GetFbxManager());
lConverter.TriangulateInPlace(node);
mesh = node->GetMesh();
now you should be able to get a correct vertex count from your mesh, and be able to extract the vertices. NOTE: If your .fbx file consist of more than one mesh then you would need to iterate thru the scene untill you find the desired mesh.
Hope this helps