1. Can you clarify what you mean by "The preview picture in the materials rendering"?
2. The lines you see will not show up when you render the scene. I think problem #1 one will also be resolved once you render the scene.
3. If you stuck a material in the first, default, material slot, then that is your Global material and it will be applied to every object you create. But you should be able to just create a new material and then apply it to any object, using the "Apply Material to Objects" button, to change from the default Global.