A trim runaway of jammed elevator does seem unusual. But as they are QRH procedures then one assumes they are conceivable. It would also explain the disengagement of the A/P - again probably uncommanded. If the rate of climb was undesirable, the initial reaction by the crew would have probably been to select Vertical Speed mode and not disconnect (unless it was extreme - which it does not appear to be).
Regarding the vertical speed values and ground speed values. I don't see too much wrong with this. We know they were in rough air, rough enough for them to not want to continue the approach. Perhaps we can expect bumps and spikes in speeds and altitudes over that time. The general trends look consistent with an initial climb, acceleration to commanded speed and then once that speed was reached another steeper climb.
Does anybody know how the Mode S system derives or calculates these values? Obviously vertical speed is a function of altitude change over time and ground speed of position change over time. If the Mode S system calculates these values rather than extracting directly from the Air Data Computer then perhaps we can expect the data to be somewhat erratic depending on the sampling rate (frequency) of altitude and position data by the Mode S system. It would seem sensible for these values to be calculated from a systems integration unit interoperability point of view. If I was the designer of the Mode S system, I think I would calculate as much as possible within the module.