1- I know different focal lengths change the depth and flatness of an objects in the picture. For examples longer focal lengths make objects appear flatter so they will be appropriate for portraits. Please see (https://en.wikipedia.org/wiki/File:Focal_length.jpg)
2- I also know that crop sized sensors have a more limited angle of view in comparison to full frame sensors. For example, the angle of view of a 35mm lens on crop sensor camera is almost equivalent to 50mm in full frame.
Given 1 & 2 from above, do crop sensors also change the depth and flatness of objects? I mean, does a 35mm on DX (Nikon) have a different perspective than FX (also Nikon). I've heard that crop sensors only change the angle of view and that they are similar to digital zoom at the center on the picture when in comparison to full frame (so they cannot change the relative depth and perspective). However I also heard that crop sensors also change the depth of field. What does that really mean?