I'm a novice on photography, so I hope I can explain myself clearly. I have a Nikon D5100 (cropped DX sensor) with kit lens, 18-55mm. I'd like to buy a normal prime lens, getting faster shutter speeds, greater aperture and overall better "normal" photo quality. Given my cropped sensor camera, a 35mm would probably be the best focal length to look for, as far as my research goes (50mm, some would argue).
And now it's when my speculation comes in: the distortion I get from moving away from normal focal lengths I suppose is mostly a factor of the focal length itself, not the sensor size. If I get a FX 10mm lens on my camera, it would give a 15mm field of view, but the fish eye distortion would remain the same, even if giving me just a smaller portion of the picture I'd get with a full frame sensor and hence not showing the more distorted outer edges, isn't it? Does that mean that with such 35mm DX lens I'll get a normal field of view and at the same time a slight fish eye distortion? And that a fully "normal" photo (field of view and minimal distortion) would only be obtained with a 50mm FX camera or a 50mm DX while standing far away from my subject?