Rio I had the same problem, however after trying different methods including a small amount of parafin oil on the top to suficate the little devils all it did is make the nutrients turn cloudy and smelly. I ended up emptying out the complete lot, encased my nutrient reservoir in black plastic.
( PS it was a large clear fish tank) this has worked very well and no more mosquitos or problems.

Ok
I may cut some foam boards to try to cover the area that is open. I am going to change nutrient soon, but I know this will be back.

You can not completely eliminate mosquitoes or algae. If you make a diligent effort to block all obvious sources of light entry you will greatly limit both. Enough that you shouldn't have to worry about them between regular nutrient changes.

Not sure about the mosquitos, but for algae you could use an aquarium UV system. Water is pumped though a light tight tube with an UV bulb in it. The UV light kills the algae. That keeps most aquariums or fishponds crystal clear.

Disadvantage, you need power and a pump.