1) Air and nitrox do get "thicker" at depth, but you have to get to about 600' before the effect is pronounced. You'll notice the increased viscosity in your lungs before you'll note any change in the performance of the second stage.
2) all second stages have a moderate degree of venturi effect - that's why if you drop a free flowing reg, it keeps right on free flowing. Adjustable flow vanes just let you increase or inhibit the effect in some circumstances
3) The valve does have to move more gas at depth, but that's simply because you breathe more cubic feet with each breathe at depth - if you breathe .6 cfm at the surface, you'll be breathing 3 cfm at 132 ft (5 times more as you are at 5 ATA). So if you take 5 breathes per minute, that's only .12 cu ft per breath at the surface, but it's .6 cu ft per breath at 132 ft, and both breaths will have the same amount of inhalation time. Consequently, at 132 ft, in that fixed period of time, the reg has to move 5 times the gas that it does at the surface. The thing is that a reg like the Conshelf XIV can move about 30 cfm.
So...if I am at 132 ft and inhale that expected .6 cubic feet needed for one full breath in 5 seconds, that's equivalent to a flow rate of only 7.2 cfm, leaving a reserve flow from the second stage of about 23 cfm. However, if I get panicked and inhale that same .6 cubic foot needed for a single full breath at 132 ft in only 1 second, then it requires a flow rate of 36 cfm and I'll start out breathing the reg and feel starved for gas - increasing the panic response. That's why panic = really, really bad underwater, especially at depth.