For magic rings which offer a passive effect, such as ring of protection, the malfunction chance is diced every time the effect is triggered. For example, for a ring of protection, a d10 is easily rolled alongside a d20, with a 1 or 2 on the d10 indicating a malfunction (and loss of AC).
Elves can move, shoot, and move again, as per the MM. More on this in Combat.
See above section on dwarves for info regarding magic ring malfunction.
Halflings receive a +3 bonus to-hit with slings and bows, as per the Monster Manual.1)
Half-elves can wear items made for humans or elves, unless the item in question specifically lists half-elves as being in a different category. 2)