If you are not injecting CO2 you won't lose CO2 with water agitation. You will pick up more, just as you pick up more O2 by agitating the water surface. So, that isn't a problem.

BGA seems to start when there is a lot of light and too little nitrate. If sunlight strikes the tank BGA almost always will start at those locations.

The algae on the glass sure seems like Green Dust Algae. And the spots on the leaves might be green spot algae, which generally means not enough phosphate.

Why not use Excel? In a 10 gallon tank Excel isn't terribly expensive, and by dosing at 1.5 times the recommended dosage you can kill off the black brush algae, if that is what is on the leaf edges, plus supply more carbon for the plants. And, you can increase the dosages of nitrate and phosphate a bit to see if that helps with the BGA and GSA. Using Excel might make doing water changes a little less risky too.

If the algae on the glass is green dust algae - if it wipes off easily it most likely is - I still like the method of leaving the algae alone for 3 weeks to make it live out its life cycle, then wiping it off and doing heavy water changes for a few days.

Look at all of this as one more way to enjoy your hobby! What fun would it be if there was never anything to do?