Yes, your temperature difference on clear, calm nights is almost certainly driven by inversion (higher temps in higher elevations to a point). For instance, last night (which was clear and calm), my low was 7.1 deg at 5ft and 8.2 deg at 20ft. That's a 1.1 degree difference in 15ft.
As far as pressure, klschmidt was right on. Given that you have a VP2 console, I'd sync to the airport's SLP reading (NOT altimeter) during stable weather (steady barometer and no cold/warm fronts in the area). If you don't know how to find the airport's SLP measurement, simply give me your airport's location or call sign and I can create a link for you. You don't want to sync to the altimeter in the winter because the further you are from about 60 degrees, the higher the SLP reading will be compared to the altimeter. At 20F, we're talking like 0.10" - not an insignificant amount.