Is it a necessity to have air stones (with an air pump) in the tank

? I've been set up for a month now, and it seems that several of my fish have died from oxygen deprivation. I have a 55 gallon tank, a Rena XP2 filter, and fish (2 gouramis, 2 red eye tetras, 1 neon tetra, 1 glass fish, 2 mollies, 1 algae eater, and 1 kuhli loach).
I thought air stones were for looks more than anything, but do I need them?!?!? My surface water is about 1" from the top of the tank, and my tank lid (cover) is covering the top pretty well.
My water readings have been steadily pH 7.6, Nitrites 0, Nitrates 0, and Ammonia between 0 and .25
(this is by a test kit)
Also, I have a sunken ship decoration in my tank, that the cloth sails are getting green and brown splotches on them, could this be algae growing on it