The difference between the elevation readings on the app versus a GPS unit with barometric pressure is to be expected. The app uses basemap data to calculate elevation, and this data often does not take into account things like bridges, elevated paths and roadways, et al. Also, as it depends on the accuracy of the track to calculate these numbers, riding through areas with thick foliage or tall structures that obscure line-of-sight to satellites can result in a track that may "climb" or "descend" more than what actually occurred on the ride.
As far as auto-stop is concerned, it's made more accurate if you have a speed sensor paired to a GPS bike computer. The speed sensor is far more immediate in its reaction to changes in motion and will more accurately measure stoppage time than relying on GPS tracking differential. The difference between when I use my Edge 520 on the Moots (which has a paired speed sensor) and, say, my Pedal Force (which no longer has the sensor) is often fairly pronounced, even though I have auto-stop configured on the Garmin.