#2, It is perfectly normal for the zoom ring to slide on its own if you point the lens up/down. That is how it is supposed to be, and makes it a very easy to use 1-ring zoom, especially for anything with action, like sports. GREAT lens. That was the lens that spoiled me for how smooth a zoom should be.
#3, As I understand it, Nikomat is the nameplate used for the cameras sold in Japan, in the US it is Nikkormat. Something about trademark in the US required the name change.