The general tiling of a sphere is very hard and I don't know there is a perfect solution to what you want.
A general solution might to pick one of the spherical polyhedrons (e.g a soccer ball with pentagons) and work from there.
As for getting at least one normal, you can create a sphere (or part of one) create a plane tangent to its surface, and sketch a square on that. After that, it probably depends on the pattern you want to create. Maybe someone else has some ideas?
BTW, you might Google "Tiling a sphere" There is lots of discussion out there on this. Or look here for some images:
