I personally think you'd be better off having your breaker box and inverter inside, where they would be more protected from the elements. At the very least the breakers should be indoors, with the panel mounted near where your power will be coming in. Surface or flush mounting is strictly a personal preference, dictated by the design of your box.
However you design the enclosure for your batteries, make sure there is adequate ventilation for the gases to disperse, and if you use flooded batteries you will need to have a way to access them for maintenance, whether opening an access panel, or sliding them out on a tray (or multiple trays if you have a large bank). Depending on what you choose batteries weigh anywhere from 50 to 125 lbs each so make sure the storage bay can handle the weight.
Generator is a little more flexible... what you do with it will depend on the physical size, where the fuel tank is located, and if it can be relocated if necessary. If it's small and light you can certainly keep it in the bay with the batteries, but if it's a bigger and heavier one you'll want to make sure the bay can handle the combined weight.
As far as the divider itself, metal studs would probably be stronger but wood can also be used, or just fasten in some sheet metal at top and bottom, that should also likely be good enough.