When an item is put onto Link's persona at any point in time in OoT, they essentially become part of him. Like when you get in a time machine, everything in there is transported with you, same effect. The nuts are stored with his items as well as deku sticks, bombs, arrows, seeds and the like. The reason why he can't use a bow as a kid is probably because of the strength needed to wield it, to pull back the string. The hookshot is probably a little too big and awkward for it to be used by a child effectively. As for why adult link doesn't use the child items... A slingshot probably wouldn't be effective against the monsters that Link comes across as an adult, same with the boomerang. Given that and the initial size of the items would make it awkward for adult Link to use effectively. In MM the items are the right size for Link, but the method of time travel is different than OoT seeing as it's used by the Ocarina and not by sealing of the soul. When Link draws the sword he's sealed for seven years and doesn't travel instantaneously, and when he puts it back, the sword reverts to the original time it was at rest. In MM he plays the song and it reverses time by 3 days so everything is how it was, aside from the items held on Link's person. He loses the small items like arrows and such because of game convenience and difficulty, that's really the only reason they did that and really can't be explained logically.