Yes, Air and ground units can kill each other. You have to understand that an Infantry unit contains infantry and all the support units that go with it. Some of the support units will include AA units. Axis and Allies is set up to be a big picture view of the war, not as much detail as you might imagine. I can understand why it becomes confusing when we have artillery, armor and infantry represented seperately. In earlier games, we didn’t have arty and it was understood they were part of the other manuver units.
Enjoy the game!