Smart Power Mode doesn't affect Indoor Location at all, but can lead to better battery life when the beacon's not in use, so feel free to turn it on (:
Yes, in SDK 2.x we've simply renamed Apple's "accuracy" into our "distance". It kind of made sense, since the general consensus in the iBeacon community at that time was that it really is an approximation of distance. However, as iBeacon started moving out of the hands of early adopters and more and more developers took interest in the technology, we felt this nomenclature resulted in many unrealistic expectations. Hence, in SDK 3.x, we got rid of ESTBeacon, and decided to stick with CLBeacon and it's "accuracy".
The beacons are meant to be positioned around chest height.
I don't think speed of movement should affect the accuracy a lot—it's rather whether you're moving at all or not. Do your observations indicate otherwise?