Yes, I get false lows when I sleep on my sensor. My understanding is that the area gets compressed and the amount of interstistial fluid decreases (as it’s pushed out under the pressure), and so the sensor readings drop. Move off the sensor, the fluid comes back, and readings return to normal.
And, also yes, the first day or two of a new sensor can be very inaccurate. I once had my Dexcom reading HIGH (> 400 mg/dl) and my fingerstick was 11.3 mmol/L (203 mg/dl). I called Dexcom and the person on the phone suggested I calibrate, but also noted that this was “normal” for the first day. As I noted in this post, Dexcom is spending the first 24-48 hours of a new sensor trying to match its data to the data you’re providing it, which is why it’s not considered accurate for the first day or so.