1) I don't feel anything interesting during exercise. I feel vague pressure and tension in roughly the expected places for a given movement, but that's about it. I don't get the sense that my body is actually doing anything in response to that movement.
2) If I make any attempt at actual intensity instead of literally just going through the motions (which does not do much to alleviate point #1), I often end up with some weird injury that flares up over the next week or two, even when nothing seemed to go wrong. Getting "brain fog" for hours after the exercise is also pretty common.
I suspect this is something to do with a broader interoception deficit (I also have trouble gauging hunger/fullness, thirst, tiredness, illness etc.), but it's hard to find any reliable information about that sort of problem. Most sources basically just tag it as an autism spectrum symptom and don't bother actually examining it.