Check valves do not function well in a reef aquarium because the critters that grow in the system also grow on the seat of the valve, preventing it from sealing. This can occur at just about any time which means even cleaning them regularly doesn't ensure they will work properly. Given this, I recommend you remove them.
In your original picture, the one valve at the inlet is not needed. The two valves going back to the sump are definitely necessary as with them the water will try to go through those instead of fighting up 3-4 more feet of vertical head pressure. On my setup, the valves to the refugium and GFO reactor are almost closed in order to send the majority of the water to the display. If I open them all the way the water doesn't make it to the display at all. The two valves going to the returns are optional IMO.
HTH,