1,circulation is not desired in a dsb, b/c you want the lower layers to remain low in oxygen, which is where the bacteria taht finishes breaking down the nitrates live, yes they DO, now sand and cc may be used, but a 3 " cc bed is not any where near the same as a 3 inch bed of sand
2, again, you do NOT want circulation in the dsb, it is the one thing you do not want, it defeeats teh purpose of having it altogether
not dogma, c allows water to pass through and so on, whihc enables the cc to trap the detritus, yes some have used cc effectively, BUT sand is more effective, and easier maintenance than cc
IMO, objective study or not, i have used both, and both on the same tank, after doing alot of research(open research, not blind guessing and trying to avoid the issue) and have found that dogma or otherwise, i have found the cc to not be a nitrate factory, but have not yet found a better description that can be understoood by lamen's and more to the point, not to mention that although not accurate, teh term nitrate factory is an oft used term so it is teh first thing that comes to mind for most( like the term airplane or military intelligence, nether is any where near a description for the item tehy name)
and another point, to have the same affect with cc, you need at least 4 times OR MORE cc than sand to have the sam esurface area, and to create teh anoxic zones desired, so 3 inches of cc is not near the same as 3 inches of sand
now that alllll being said, like i menitoned above, there are many cc users who have had no problems( i agreee, kris), but htey do involve more maintenance and are not quite as affective in the long run as sand(for he same volume)
BUT
they can work well
i myself, as mentioned have used both and now only use sand, by choice, and i do reccommend it, but cc CAN be used, howveve rit is more a thing of the past with most of us, many of us have used it but if we had it to do over again would definitely consider using sand the next time(if we have not already switched yet
HTH and good luck