Rabbits can eat apples, but bunnies shouldn't.You should not give your bunny ANY fresh foods unless they are at least4-6 months old. Young rabbits have very sensitive digestive systems andcan not yet handle fresh foods. When they are old enough, you cangradualy introduce them to veggies, but fruits should be limited tovery occasional small treats. Fruits are high in sugar (as well ascarrots). Sugar is hard on a rabbits digestive system, very fattening,and if given too much, it can cause an overgrowth of the bad type ofbacteria in their gut.
I hear apple branches are good for chewing. Just make sure they haven't been treated with any sprays or pesticides.
And I just gotta say that your bunny is adorable!!!