I'm not THAT into maritime engineering (I'm an avionics guy, most of my structural knowledge, such as it is, relates to airframe structures)!
I simply am aware of some of the terminology, and have a very superficial, passing acquaintance with the meaning and use of some structures (mainly what you get from reading things like D. K. Brown's
Rebuilding the Royal Navy).
As for your questions, I'd suggest the following as strictly amateur (and possibly mistaken) opinions:
For submarines the external framing allows maximum useable internal volume for minimum pressure hull diameter (crush depth being somewhat related to p-h diameter, the smaller the deeper). Additionally, this makes "double-layer hull" construction easier, which aids streamlining for ballast tanks and other external items, as well as providing a degree of damage-reduction due to the unpressurized outer hull reducing the pressure-wave hitting the pressure hull from depth charges, torpedoes, etc.
Internal framing is easier to build but restricts internal volume, makes streamlining harder, and is best for "single-layer hull" designs.
I
think (not know) that you can get a lighter ship structure by increasing the hull plate thickness while decreasing scantling strength (good for displacement-limited designs, as well as reducing material costs for merchant designs), while stronger scantlings are more damage-resistant, and can support heavier structures (like armor plates, gun turrets, etc).
Transverse vs longitudinal relates to expected wave heights & periods, with transverse reducing twisting while longitudinal reduces bending along the ship's axis when the bow & stern are lifted by a wave but the amidships is over a wave trough (and vice-versa). A ship intended for high speed in rough seas absolutely needs both, as do long & narrow ships like destroyers.
Armored-belt ships have less need of longitudinal, as the belt adds strength in that area, while armored-deck ships need less transverse as the deck armor substitutes partially.
"Ship strength girder" is the combination of hull plating and framing which provides longitudinal strength. An example of this, and of differing approaches, is to compare USN pre & mid-WW2 carrier construction vs RN ships.
The US had the hangar deck as the "strength deck" (the upper-most deck which provides structural rigidity) with the hangar and flight deck being non-strength "superstructure". This requires fairly heavy hull framing due to the great length vs "depth" (height) ratio, but allows easy modification of the above-deck structure (like moving elevators from centerline to deck-edge).
The RN had the flight deck as the strength deck, with the hangar sides providing part of the hull girder along with the lower hull sides. This allowed lighter scantlings due to the better length vs "depth" (height) ratio, but made moving elevators to the deck-edge far more difficult. HMS Hermes was modified after launch with her fore elevator moved from the centerline to the port deck-edge... this required extensive changes to the port hull structure below the hangar deck (and, I believe, to the flight deck support structure on the underside of the flight deck) to compensate for the loss of girder strength from the cut-out in the hangar side for the elevator.