Well....
About the floating rocks, if we can guess that the 'vwoom' of sorts was part of an activation process for the War Sphinx model, then we can assume they were, scientifically, floating due to electromagnetism. The rocks themselves could be metallic and be highly magnetic, and any simple electrical charge upwards and outwards, especially one that could've been "charging" the sphinx over some time, could possibly levitate them.
Chief wouldn't, of course, because he weighs 2 tonnes rather than a few grams.