#2 Yes, that's normal, but, some of the copies I've dealt with have been so loose that it would slide even when the lens was pointed downward at a 15 degree angle.
#3 Actually, it involves Zeiss-Ikon in Germany. They filed a lawsuit against Nikon, claiming trademark infringement, since Nikon sounded too much like "Ikon", and Nikomat was too close to "Ikomat" for their comfort. Hence the reason why Nikon F's were sold as Nikkor F's in Germany, and Nikkorex bodies were also sold as Nikkor bodies (the Nikkorex F became the Nikkor J - Nikkorex was too close to Icarex in their opinion). Nikkormat bodies sold there didn't have the "Nikon" inscription on the back of the camera, instead, only saying "JAPAN".
By the early 1970's, the lawsuit was either dropped, or Nikon paid whatever Zeiss-Ikon wanted, and Nikon was allowed to sell the F as a Nikon F in Germany. At the same time, the Nikkormat began being sold with the regular top covers that said "Nikon" next to the eyepiece. Happened at the same time as Nikon going from "Nippon Kogaku Japan" on their lenses to "Nikon".