Sports GPS devices not (generally?) precise enough to locate your position on Earth to the nearest foot. Trees, buildings or other obstacles between you and one or more of the satellites will reduce the precision. If it estimates your position at X one moment and X+10' three seconds later, that change in estimated position results in speed greater than zero. That sort of drift is usually irrelevant to your sporting purposes.
In your settings you have the option to have the recording pause when you're stopped, or your speed is below a custom level. Using that will filter out that drift while you're stopped, at least in the GPS recording.
With respect to the additional sensor -- be sure that you are paired to use the cadence/speed sensor for speed.
Yes. It's a fundamental limitation of the precision of the GPS itself. There's a error in position and it drifts over time. Movement over time translate into a speed. It can be up to several MPH and enough to trigger the auto-pause if moving at slow speed or un-pause it when stopped. Garmin provides for a wheel sensor because it can help improve this, among other things.