Why does each skill say, "increases quiver size and increase arrow by 1"? I don't see a difference. Ive tried resetting my stats but my arrow count is still 10 whether I have points in arrow abilities or not.
Each skill says that because, at least from my experience, investing in bow skills really does increase the amount of arrows you can fire in succession without having to wait for them to reload.
I remember starting the game with 3 (or was it 5?) arrows available for firing before having to recharge, and now I have 3 times as much available to me. Did you start the game with an arrow count of 10? That seems very unlikely.
Regarding the amount of arrows not resetting when you reset your skills, that could very well be a bug. Are you still able to fire 10 arrows in a row after resetting your skills? (it might be that the visual representation remains "stuck" at 10 arrows, but you lose the actual benefits of the skills you have).
You begin Kingdoms of Amalur: The Reckoning able to fire 5 arrows between reloads. After a short time without firing any arrows, regardless of how many shots you fired, your quiver will refill itself.
There is one tree of bow abilities consisting of 5 abilities. The general ability description say, "Increases the number of arrows that can be fired before reloading" and "Also increases the size of your quiver," but these only refer to the first point in each of those respective abilities as only the first level of those abilities bear the description, "Increases quiver size by 1." This means that you can at most fire 10 arrows between reloads with a minimum of one point in each bow ability. These abilities also grant you further arrow abilities such as increased damage, increased piercing damage, arrow storm, a bleed effect and a scattershot and further points will increase these effects.
Unbinding your destiny, thus removing the points in these abilities should decrease the number of arrows in your quiver, but because of a defect in the game, it does not. This happens to me as well. This could be used to minor advantage when trying out different destinies by increasing the size of your quiver, but will only matter if you use the bow and don't plan on investing those points in the bow skill tree anyways. Re-investing points in the bow skills will not increase your quiver beyond the maximum of 10 arrows.