Ammonia "practically" zero is not good. If it is anything but zero, you are still cycling your tank.
If you are not cycling your tank, you should test for phospahtes. And we need a nitrate test too.
Regardless, start running a phosphate remove such as rowaphos or similar.
Any algae eating fish CAN eat hair algae, but it is usually their least favorite
Lawnmower blennies, foxface rabbitfish, some tangs will eat it. The best animal is a sea hare, but you wont have enough to keep it alive very long so I dont recommend it but for a really large tank.
Physical removal will help as well.
Are you using RODI water for top off?