Did take a peak at the picture, and the first thing I'd recommend is taking the check valve out of the return line from the pump.....In all honestly they do nothing more than cut flow (to a degree) and provide a false sense of security against back siphoning........They do fail at some point, so really not worth the money, when you can accomplish the same thing with other cheaper methods......
As far as your drain lines coming from the tank to the sump.....Ditch the valves again.....You don't need them there, and if your intentions are to throttle things down your opening yourself up for disaster....That plumbing design isn't designed correctly to throttle them that way without a emergency backup......
As far as skimmer placement and return pump placement, I'd opt to move the skimmer into the compartment where the return lines drop down into the sump. You could/might have issues with the skimmer putting off micro bubbles and in turn they would probably be sucked up by the return pump and shot into the tank.
Another issue is your going about your flow theory IMHO wrong with trying to get 15x turnover rate through your return pump....There are several theories on flow rate through the sump......Most will say or suggest 3x-5x turnover rate of the system through the sump......Your other flow (turnover rate) is achieved actually inside the display tank by various means......