Generally, large bows draw slowly and do more damage. So short bows, fast and low damage, long bows slow and high damage, other types in between.
No.
The medieval warbow, as we know it, wasn't an effective weapon when aiming at individual targets, as the power of the bow would not permit you to hold it long enough to properly aim. Like so: http://www.youtube.com/watch?v=3wBdXcbxrJg. Although you can see him hit two out of three shots at eighty yards (73 metres), which is really quite good, but the real effectiveness of the bow was displayed in the battle of Agincourt/Crécy; lots and lots of unaimed arrows fired into the opposing army to hill or stun any of them. The longbow now is drawn differently. This technique is called "drawing the bow", instead of "bending the bow";
"the Englishman did not keep his left hand steady, and draw his bow with his right; but keeping his right at rest upon the nerve, he pressed the whole weight of his body into the horns of his bow. Hence probably arose the phrase "bending the bow," and the French of "drawing" one.
—W. Gilpin."The French used to "draw the bow", which means that you don't use your back muscles as much as your biceps. This is a more accurate technique (which is also the more modern technique, and with longbow shooting is called "target shooting"), but it cannot be used to draw heavy bows, as the stress on the arms and muscles would be too big.
What I'm trying to say is that you can't categorise bows. It completely depends on what Bethesda chooses. You can compare longbow shooting techniques to throwing stones/balls: you can throw them very far, with a lot of force, but not accurately, and vice versa.
The upside of having a crossbow is that you can shoot bit darts really far with a lot of accuracy, as you don't have to keep the bow drawn, but the heavier the bow, the harder it is to reload (with the same technique). I know someone who owns a shop which sells bows (Fairbow, but it's all in Dutch), including crossbows. His heaviest one has a draw weight of 800#, which is enough to stop a galloping horse (and probably an elephant too). He has shown me how he draws it (with a crank), and it takes about half a minute. In all fairness, if that half minute is over, I wouldn't want my house to be on the other end of that thing.
Shortbows (I'm talking of D-shaped ones) aren't used because they break. Shortbows (like horse bows, which are actually called composite bows) are very different to longbows. A longbow uses the strength of the fibers in the wood to compress and stretch them, while a composite bow uses materials which are easily stetched and compressed (like sinew and horn), and thus uses the springyness of the material rather then the compression of fibers. This means that while a longbow is heavy, it draws gradually or builds up, i.e. when you start to draw it there's not a lot of force, but when you reach your drawlength, all of the force is there (if you plot draw weight versus drawlength, you will sort of get a straight line which runs through the origin). The composite bow doesn't do this. It is really agressive, in the sense that it doesn't build up, but starts right away with nearly all the force you have to pull at the end (if you plot draw weight versus drawlength here, you will get a curve which looks like a logarithmic function). The consequence of this is that the longbow is slower for the same force as the composite, due to the fact that the string of the longbow (when it is released) will push the arrow with the full force at the beginning, but that force will decrease quickly, while the composite will keep pushing the arrow for longer, with a comparable force.
You also say that short bows are fast but have low damage, and longbows are slow and have high damage. This is partially true, but that's only because longbow archers use heavy arrows, as they need to be able to withstand the first impact when the string is released. In essence, speed*mass = damage, so the damage of the longbow and composite bow are about the same (when looking at bows with equal draw weight). BUT, since composite bows have a different force curve (the logarithmic function as opposed to the linear one), the arrow will fly at greater speeds, so effectively, the composite bow is faster and provides more of an impact and is thus more damaging.