A means Auto, being that they can be used on Auto Exposure cameras such as the ME or the LX, which have Program and Aperture priority exposure settings.
The K1000 is a completely manual camera, so it doesn't need the A setting, but it can still use any A designated lens flawlessly. You can't use an ME very easily with an M designated lens. It just won't work right. (call me out if I'm mistaken - as I've never actually needed to worry about this)
Pentax k-mount doesn't need element adapters with an EOS camera. Neither does Nikon, Olympus, M42, Contax/Yashica, Leica R.
NEX is a mirrorless system, and doesn't need a glass adapter with really anything, unless that is you want to make something full frame, like with the Metabones adapter- which gives you the FOV of a full frame lens on a crop sensor body like an NEX (as well as allows you go get like f1.0 out of them, which is fucking silly shit)
You shouldnt spend more than 10 bucks on any pentax adapter. I have like 5 of them and I paid maybe 20-25 for the lot.