You can only fire at planes the same altitude or plus or minus 1; but in the case of a difference in 1 altitude you can only shoot up to half the ruler at the enemy plane and it is treated as if it was further than a half ruler away for damage. Altitude makes a bigger difference when there are ground objects and objectives. They can only shoot up to altitude 1 and same with planes shooting at them with the exception of bombs (note that planes can fly at altitude 0 if they have at least one climb counter).
Each plane has a max altitude and climb rate. You can find those in the "Balloon Busters" and "Miniature" rules in the support section and it will also be on a card in the deck of series 4 miniatures. Climb rate is how many times a plane needs to use the climb card in order to gain an altitude level (thats what the climb counters are used to keep track of).
Most of the other counters are for objectives. So the camera and bombs are for successful missions of those types; put the counter on the ground target to show it. The machine gun counters are for showing a trench machine gun has been silenced. I don't know if there is any point for the airplane shot down counters but it might just be for fun to show where they crashed.
Another thing altitude affects more is 2 seaters. The rear gunner has a blind spot because of the tail of the airplane if the target is at the same or lower altitude; if the target is at a higher altitude then there is no blind spot.
One more thing to remember is that climb counters don't mean anything other than how soon the plane will get to the next altitude. So for game purposes there is no difference between a plane at altitude 3 with 1 climb counter and another at altitude 3 with 4 climb counters. They are simply both at altitude 3.
Hope that helps.