Will an actual Nikon lens fit on a Nikkormat FT?

I'm thinking of purchasing a Nikkormat FT in the near future, but before I do I need to know something: will a more modern Nikon Lens fit on it? E. G.: Zoom-Nikkor 35~80mm f/4~f/5.6D.

Yes it will since its an FX (full-frame) lens. A DX (crop sensor) lens could be used on your Nikkormat FT but with heavy vignetting because the image circle of a DX lens is too small to cover a 35mm film frame. As long as you use FX lenses you should be fine - as long as the lens has an aperture ring.