Focal length effects

Something I've been trying to understand for a while now. What does focal length actually do?

Of course, I understand the narrower field of view of a longer focal length, but imagine for a moment your sensor had infinite resolution. If you were to frame a portrait with an 85mm lens on full frame, and then from the same position used a 50mm lens of the same aperture and then cropped using your infinite resolution sensor so the framing matched, would there be a difference between the two images? Is the longer focal length affecting DoF or is it just the subject distance?

And in a similar scenario, if you had a medium format camera (of the appropriate size) with an 85mm lens and a 35mm sensor with 50mm lens so the FoV was the same for both, and with apertures set to provide the same DoF and you took two images from the same position, aside from 'quality' differences potentially afforded but the MF sensor, would there be any difference? Does the longer focal length lens have any inherent properties that would render the scene differently?

Thanks to anyone who can help answer this for me.