Gas exchange (O2/CO2) occurs at the capillary membrane of the aveoli, the terminus point of a decreasing diameter branching system; it's not a loop. Breathing in and out exchanges all volume in the lungs, with each breath, (in layman terms as there is some residual volume that does not exchange). Imagine trying to create this same exchange with fluid, in tissues as delicate to over-expansion as the lung. How else could you do it without compression and expansion of the lung.
Wet drowning victims (those whose lungs fill with water) often succumb to secondary drowning, aspiration pneumonia, as the result of irritation of the lung tissue. The same would probably occur with liquid media and is probably the cause of deaths post experiment considering the irritation involved in liquid tidal flow.
The machine used for taking O2 out of water is called a mechanical gill.
All your questions re gas transfer will ultimately show that liquid media seems too complex for human use and would probably be bypassed by heart/lung machine technology to perform extra corporeal perfusion, thus bypassing the lungs altogether. This basically is a blood scrubber, in the same way rebreathers use air scrubbers. The technology exists and is already routine for surgery.
Mount one on your back, plug yourself in using large bore catheters, and forget about breathing altogether. You could do it today if you wanted to. All you need is a doctor, a machine, and a bathtub.