The nickel plating is actually triple plating of nickel-copper-nickel. The layers are Ni: 5-6µm, Cu: 7-8µm, Ni: 5-6µm, for a total thickness of 17-20µm.
Neodymium magnets are a member of the rare earth magnet family. They are called "rare earth" because neodymium is a member of the "rare earth" elements on the periodic table. Neodymium magnets are the strongest of the rare earth magnets and are the strongest permanent magnets in the world.
Disc, cylinder, and sphere shapes definitely cannot be manufactured this way. Rings magnetized this way are referred to as "radially magnetized", but it is not currently possible to manufacture neodymium ring magnets this way. We are working on it, however.
Not unless you really work at it. While you probably don't want to stick magnets directly to your computer case, having them nearby will not harm your computer. Magnets can damage floppy disks and magnetic tape storage media, so you must keep magnets away from these items. They should not, however, damage any data on your hard drive unless you place a very large and powerful magnet directly on top of the drive. Every hard drive already contains a powerful neodymium magnet, so one moving around outside the case will not affect the data.
The grade, or "N rating" of the magnet refers to the Maximum Energy Product of the material that the magnet is made from. It refers to the maximum strength that the material can be magnetized to. The grade of neodymium magnets is generally measured in units millions of Gauss Oersted (MGOe). A magnet of grade N42 has a Maximum Energy Product of 42 MGOe. Generally speaking, the higher the grade, the stronger the magnet.