Re Airstones

There are no real benefits to air stones provided that the filter moves the water round the tank. Air stones are mainly because the fish keeper likes the looks of the bubbles.
But there is one circumstance that air stones are useful. In very hot weather or when the tank temperature needs to be increased to treat sick fish (eg for whitespot) the bubbles from an air stone help churn the water better than a filter alone. Warmer water holds less oxygen so more water movement means more water exposed at the surface so gas exchange can take place better - that is oxygen into the water and carbon dioxide from fish respiration out of the water.

If you are thinking of an air stone in Moonbeam's tank, don't forget that bettas like calm water so you don't want to make any water movement too much for him.

Just a mad thought... If it were very hot weather (never been known here) the air going in to the air pump will be warm, perhaps 10°C warmer than the tank and it will add to the tank temperature. If you were to put the air pump in a sealed box, make a hole in it and fit an air inlet tube the tube could be put in the coolest part of the house like the void under the floorboards or the fridge or even the freezer. A slow flow of -15°C air would certainly cool the water, I haven't bothered to do the maths to find out how much cooling capacity this would have but if anybody is interested I could do it.

@Matt I had thought about that, the inner tube from a biro (sans ink) would pass between the rubber seal and the door without being flattened... you are not contemplating doing this are you?

I've got them in both my tanks.

My 120L has good surface agitation so the airstones are completely unnecessary but I put them in at the beginning before fully understanding their purpose.  They stayed because all good aquariums should have bubbles somewhere (in my head, anyway)!

My little Flex 34L is another matter entirely.  I've had no end of problems with losing fish to dropsy.  The shoal of CPDs I have has 2 distinct types: proper full-bodied ones and a load of scrawny ones; they are slimmer and sort of hollow bellied and it's these runts that have been giving me trouble.

The water quality is good, levels are 0, 0, 0 (Bio Nitrate-EX) and the shrimp are breeding nicely, but the runts were gasping at the top and the stronger fish were seeming listless too.  The only thing I noted was that the gills on the runts were a little pink.  It then occurred to me that my efforts to tame the whirlpool effect had taken away all surface movement so, out of desperation I dropped in an airstone.

24 hrs later, the tank is transformed!  Fish are active and colours are better already.

I just wish I'd worked it out earlier as I could have saved two or three fish from an early grave 

I keep meaning to do a review of the Flex.

It needed some work to make it suitable for small fish and shrimp because of the absurd jet of water from the pump that forced the fish into one corner and the massive openings to the filter compartment. Overall I'm very happy with the tank now though.

Going by your description though, I think you are talking about the Fluval Edge and I can't comment on that one!