The diameter is 55 mm. So you could use this item: Hoya Digital Filter Kit II (UV, CIR-PL & ND8) Filterset (55 mm, ND- / Graufilter, Polarisationsfilter, UV-Filter)
If the lens has an 82mm filter thread, then yes. Nikon must make over 80 different lenses with different filter threads. We have no way of knowing which one you have
You can't screw a filter onto a camera. You screw it onto lenses. And we don't know which lens is mounted. This set can be mounted on lenses with a diameter of 58mm.
According to the overview, this filter set is not available at digitec.ch. I wish you a good start and hope that you will find what you are looking for elsewhere.
Yes, they are. You have to make sure that the lens has a matching thread at the front, and not a fixed lens hood. And of course the correct size of the lens, which is labelled with a Ø number on the front of the lens.