Both drains should run to the skimmer section. Feed the "fuge" with a tee in the return line. Feeding with a drain will create problems with fall out, that are not good for a "fuge," and an in-sump "fuge" is not really as helpful as many think.
The skimmer could very well require a 9" water depth in the skimmer section, as more often than not, the specs are very similar to "in-sump" skimmer stating 8" - 10" water depth. Nothing really changes, with the skimmer outside the sump. There really would be no point in increasing the water depth in the skimmer section, as it will only decrease the extra volume available for power out drain down.
Raising baffles won't increase sump volume for drain down, lowering them would, however. Overall, the sump should only run ~ half full, within the constraints dictated by the needs of the return pump, and the skimmer specs. The "fuge" volume on this small a scale is irrelevant.
The return section does indeed need to be larger, and should be large enough to run several days without the pump running dry, which can and does damage the pump. That is regardless of whether or not you use an ATO system. That is volume above the point where the pump starts sucking air, which damages the impeller and volute in the same manner as cavitation. Evaporation rates very from location to location, and other variables, however the average is 2 gallons per day. A 6 gallon return section would be a little small. To make the section larger, you go wider/longer, not necessarily higher. Reduce the size of the skimmer section and "fuge" to get the volume needed.
No need to run the skimmer output to a point outside the aquarium, because more water will flow past the skimmer than go through it at any given flow rate, it is hardly going to recirculate. Ultimately what will be more beneficial will be increasing the flow rate through the sump well above commonly recommended
