Yes, you can do like you want on the 'up and over', but you'll want to upsize the pipe to 1.5" if you can. Apparently, the gen-x will loose quite a bit with 1" up and over.
Using the other one as your drain would work, provided the bulkhead is the same size as the drain from the skimmer (1.25" I think, might be 1.5"), but I would draing the skimmer into the second compartment as not to reskim the water you just skimmed.