Trying to put down everything would require about 12 PhD theses. Lets try a primer then you can follow up with more precise questions.
Skegs are a particular hull configuration aft. Normally, the prop shaft emerges from the hull plating and is carried aft on supporting struts to the screw. In a skeg arrangement, this is filled in so that the shaft runs through a downward-pointing finger of hull plating. There are several reasons why this is done.
One is to provide protection to the shafts from combat (particularly torpedo) damage. A skeg will not save the shaft that gets hit but it will deflect the blast downwards and save the shafts on the other side of the ship. Also, it will (hopefully) hold the shaft more rigid and prevent the shaft from getting bent while it rotates at high speed. If that happens, it is an unmitigated disaster - the rotating shaft will rip the guts of the ship open (as happened to POW).
The protection provided by the skegs is a lot more significant than just helping to defend the shafts. A twin-skeg arrangement aft enables the area between the skegs to be hollowed out, reducing its cross-sectional area (thus resistance). This means that the hull can be widened out in that area, moving the magazines inboard, significantly increasing their protection. This also means that protection for things like the steering gear can be improved.
Secondly, the skegs will help the water flow smoothly over the hull and propellers aft. This is a critical function - the propellers do not function properly if they are trying to rotate in turbulent water. That is an understatement - they may not work at all or even damage the ship by causing excessive vibration. On the Cutter I was on yesterday, it was almost impossible to stand in certain places on the fantail due to intense vibration from the screws. This was enough to cause hatch covers and other fittings to rattle loudly enough to drown out speech.
Two ships illustrate these uses of skegs. The North Carolina class had skegs on their inboard shafts that were for purely protective purposes (note that the orientation is towards improving armor defense of the magazines - skegs on the inboard shafts will do little to help against torpedo attack).
On the South Dakota class, the skegs are on the outer shafts. Here, the motivation was purely hydrodynamic; the skegs ensured that the hull cross-sectional area decreased smoothly as the design went further aft. Even though this arrangement appeared to offer better protection to the shafts than the inboard skegs arrangement, this is purely fortuitous. Any enhancement to protection was purely an afterthought.
So, skegs are good, right? Well, sometimes. The problem is that the waterflow between the hull, the screws and the skegs is completely unpredictable. Nobody, and I do mean nobody, fully understands what actually happens at the rear end of a warship. Tank testing with models helps but there are scaling factors involved in there that nobody fully comprehends. A ship model can work just fine in a testing tank while the full-scale ship can develop horrendous vibration. This happened with North Carolina and it took almost two years to sort-of cure. The power loading of the screws is critical also; this is the amount of power applied to each screw by the engines.
Skegs seem particularly prone to causing severe vibration, probably because they have such a dramatic effect on water flow that it outweighs other effects. Several later German battleship designs had extremely large skegs aft overtly to protect the screws and rudders from torpedo attack. A close look at these designs shows that the designs in question could not possibly have had that effect (they may even have made matters worse), and I suspect the real reason, as with the US ships, was to improve hull width at the rear end of the ship. German hull designs were very fine (we'll define that term in a moment) with the result that the torpedo protection at the ends was very defective. The skegs on the later designs would have cured that problem.
Now we come to rudder placement. Some of this we covered earlier so I won't repeat. Like the screws, the rudders work best in smooth water. However, the very act of turning the rudder causes extreme turbulence. You can do a little practical experiment that shows this if you have a bath with a detachable shower hose. Half fill the bath, then hold the hose underwater and turn it on full blast. That will simulate the stream of water from the props. Now, hold your hand so the fingers are together and pointing straight down. That simulates a rudder. Lower your "rudder" into the water stream and start to turn your hand from side to side as if it is a rudder and you'll feel the vibration shaking your fingers.
If this is bad enough, the vibration can damage the rudder post while the exceptionally turbulent flow off one side can cause extreme vibration in the screws on that side. It's not unlike an aircraft wing stalling - and just as dangerous. There are various things to do about it including balancing the rudder but the best place to start is to ensure that the flow of water off the screws does not go near the props.
If the rudder is going to be any good it has to have "authority" that is, it will be effective enough to turn the ship. The larger the ship, the more authority is needed. Authority is increased by size and by being in smooth water, it is decreased by being in turbulence or stagnant areas. The latter are nasty. Sometimes, the flow off all the junk aft will interact so that patches of water actually do not move at all. Since the rudder works by operating on moving water, a rudder in still water has NO AUTHORITY AT ALL. This is a tricky situation since stagnant areas only form at certain speeds and the captain only finds out about them when he is heading flat out at a harbor wall and he finds his steering doesn't work. This tends to be a career-limiting situation.
If there is a big ship, it may help to divide the rudder into two smaller ones and work them together. This is not as easy as it sounds - the mechanism is very similar to front-wheel steering on a car (CEN - your assistance needed here!). Twin rudders have problems all of their own.
Its even possible to have triple or quadruple rudders. The style usually is (these days) to place a rudder in the water pushed back by the screw (the screw race). This used to be a very risky design gamble on vibration grounds but computers have made it a lot more palatable.
On drag, we have lots of fun. Basically (and this is very basic) drag on a hull is related to changes in cross-sectional area. The more slowly the cross sectional area, the lower the drag. A hull with a very low rate of cross sectional area change is called a fine hull, one with a very rapid change is a bluff hull. The problem is that fine hulls are inherently weak, especially at their ends (remember the lecture on stress?) while bluff hulls tend to be stronger.
There are lots of tricks that can be played here. It is possible to convince the water that the hull is finer than it is (skegs and other tricks). It is also possible to chop the stern of the ship off so that it ends abruptly (a transom stern). Water can't understand this so it acts as if the end is not chopped off and treats the hull as if the rear end is optimally fine. This dodge saves both weight and drag. It also creates a large stagnant area aft which can cause some serious problems. Back in the 1920s the British built a minelayer with a transom stern, HMS Adventure. This was brilliantly designed so that the mines were laid into the patch of stagnant water- where they bobbed along aft of the ship until they got sucked into the screws.
Again smoothness is critical - the hull has to be designed so that water flows past with as few disruptions as possible. That is why hulls use long smooth curves rather than abrupt discontinuities (usually - there are exceptions). The hull design has to direct water smoothly into the props and over the rudder and allow the races from those bit to be carried away smoothly. Furthermore, the water flow has to follow those hull curves and not separate from them - that can cause hideous problems all of its own.
None of these factors is independent - change one and it has impacts
on all the rest. That is why nobody really understands what happens at
the end of a ship - its just too complex to be understood. All the designer
can do is make his best guesses, try it out in a tank and pray. Then build