I personally love the Bow and Arrow approach of Far Cry 3, although I find it to be completely overpowered (OP).
The quick answer to all of your questions, so as not to bury my answer in a wall of text:
Will arrows fly further or deal more damage if the Recurve Bow is drawn longer (similar to Skyrim)?
yes to distance, no to damage.
Do arrows always hit the center or a specific point of the crosshair/sight or is its accuracy affected by the bow's draw length?
Accuracy is affected by draw length to a small degree.
Now, to explain in depth my answer to your questions.
Will arrows fly further or deal more damage if the Recurve Bow is drawn longer (similar to Skyrim)?
There are 3 different types of arrows that I have come across so far: Normal, Fire and Explosive.
Normal and Fire arrows, when draw to full length will cross the same amount of distance. Explosive arrows cover a further distance for some reason, I have come to terms with it being a bug.
No matter how far you draw your bow to shoot Normal or Fire arrows, they will kill a person in one hit. Even if you hit them in the foot, the one exception being Heavy Armored Pirates. I know this to be true as at point blank I can quickly draw and fire and arrow, then watch annoyed with the OPness of this act as they die. Fire arrows having the added benefit of possibly causing a large wildfire and catching any of your targets buddies on fire as well. Although note, it seems to affect animals completely different, almost like the developers had intended the Bow and Arrow to be balanced but for some reason its only balanced when hunting. As you may have already noticed that the bigger animals will usually take more then one hit even when struck in the head or chest. Explosive arrows kill anything near the explosion in one hit, besides Heavy armored Pirates.
Do arrows always hit the center or a specific point of the crosshair/sight or is its accuracy affected by the bow's draw length?
I have found this hard to judge as there is a pretty realistic weapon sway present in Far Cry 3. Weapon sway being the figure 8 your sights will created caused by the artificial breathing your character does. The accuracy present in Far Cry 3 is only present when "firing from the hip". As when aiming down your sites you will hit your target "60% of the time everytime", no but seriously you will hit your target everytime when aiming down your sights. Unlike FPS RPG games such as Borderlands where accuracy is the percent chance your bullet will be straight and true.
Although, they have made arrows affected by distance by adding a somewhat realistic drop. So for example, when firing at a target 25 meters away you wont experience much drop if any. A target 50 meters away however you will have to adjust your sights properly to account for the drop. Of course this all takes some practice, and for some reason Explosive arrows go further then Normal arrows.
Best Answer
Try to reload a older save or just continue your mission and go to sam in the village. Maybe you had to drop your weapons, but you don't need them right now.