Speed Sensor on a Fat Bike

It's hard to give a good answer. It depends on where you're riding. If you're riding over flat snowy fields or open roads, then GPS is almost as good as a sensor, and as a practical matter the difference should be negligible. (That's certainly true on a road bike on open roads.) If you're riding in a forest in the mountains, a place where it's challenging for GPS anyway because satellites are being blocked by trees/leaves/etc., then the speed sensor will probably be more accurate. Ideally if you can do a roll out beforehand (actually measure the distance one wheel revolution covers when the wheel is fully weighted) that would be the best you can do, but with soft tires the effective circumference is changing with every bump, so it's really hard to say for certain which is better. Personally I have speed sensors on all of my bikes, and if I had a fat bike, I'd probably use one on it, too.

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I've changed air pressure (usually lowered) mid way through a ride, it would be tough to calculate rollout when doing that... I do have one on my road and mountain bikes too, but the pressures stay constant on them.

I'm wondering if the auto-calculate picks up discrepancies...

I don't think they calibrate very often, but it's hard to say since the devices never tell you. My impression is that it's a once every few rides type thing, but I may be wrong. The only time I was sure it happened was when my Edge 800 miscalibrated during a ride and read fast/long. Since then I've always used manual calibration. I don't think you can rely on it to fix short term changes.

I believe the setting is continuously monitored and updated multiple times during a normal ride. You can periodically check the setting during a ride and after to confirm that.