The thing you are writing about with plants throwing off oxygen bubbles is called pearling. There is some disagreement as to exactly why it will happen in one case but not another. I think it has to do with saturation of oxygen levels in the water, but I am not for sure.
Hair algae is pretty lame. I only get it is tanks that don't have co2. Excessive lighting could be your first problem, but also you need to be sure that you have adequate co2 levels in your tank. Saying it is 2 bubbles per second doesn't mean anything because that is different for every person. How are you diffusing your co2? What kind of circulation do you get in the tank?