from the sound of it your tank has probably got highly toxic levels of ammonia (though you will know for sure when you get a test kit) that could be what killed the crayfish.
in new tanks its necessary to "cycle" the filter to build up good bacteria which removes toxic ammonia and nitrite from the water.
the water conditioner won't be likely to affect that as most just remove chlorine from tap water they don't affect ammonia and nitrite.
ammonia is produced by fish waste and by any excess food rotting in the tank, so it builds up more and more daily.
it is recommended to carry out a fishless cycle. which is where you run the empty tank and add ammonia to allow the build up of bacteria. when its fully established you can add the fish.
unfortunately most LFS do not know and/or care about this. their aim is to get you to buy the fish as quickly as possible (impulse buys).
if you do add the fish straight away, you still need to cycle the filter, but it usually takes a lot longer. and because the fish are in it they are slowly being poisoned. so you need to do water changes EVERY DAY!
once a week is fine for an established tank, but in an uncycled tank you need to do far far more to keep the ammonia levels low.
the airstone is the little rough black thing that attaches to the air pump tubing yes (they come in various different shapes and sizes) it will increase the surface turbulence which will increase the oxygen dissolved in the water, making it easier for the fish to breathe. so probably a good idea to turn it on constantly for the moment. the appearance is less important at the moment except as an indication that things are not right. when your water parameters are sorted out it will be easier to keep it looking good.
by the way do you have any live plants in the tank? as they will use ammonia and nitrites to grow which would reduce the toxic levels somewhat and also reduce the nutrients available to the algae which is turning the water green.
also for future reference you shouldn't really keep crayfish(blue lobster) with fish as they will get eaten (the fish that is)
ok enough waffling, sorry if you know all that already. hope it helps (and makes sense!)