The reason you have HA is that you have a excess of nutrients in your water.
hate to say it but don't trust your LFS on test results, test your self.
One of the requirements of having a saltwater tank is having decent test kits, Po4, No3, ALK, CAL, MAG and PH to start out with.
These 6 will tell you plenty for what's going on with your tank.
No3 at 10 doesn't tell me much as I don't know your Po4.
Lots of ppl now days run their No3 around 10 now days as corals need nutrients, 10 ppm might be a little to much for your tank.
In order to drop that water changes is good, having a good skimmer, feed less, running a fuge with macro's and using nutrients reducing reactors as GFO or Bio-pellets.
I would start with the simple method as you already do so in water changes but you need to know what's in that water.
If you test 0.0 TDS your good if you go above that it shows that your RODI has or can have nutrients in there as you need to test for that.
Once you got that straighten out you will feed less, even your fish asking for more food one small feeding can be enough a day to get your nutrients under control, even skip feeding your fish for a day isn't that bad.
Now your red stuff can be a bit trickier as we don't know if this is cyano or not.
Again you need to test for that.
How..............
Take a portion of that red mat you see in your tank and place it into a cup with about 2 cups of tank water.
Now add 1ml of 3% hydrogen peroxide
Over the course of several hours you may start to see a change in the water and the color of your sample.
If in fact it is the common cyanobacteria and not spirulina the water will start to turn a pink color and the sample with start to turn a green color.
Now if it is spirulina there will be no change as h2o2 has little effect on the individual cells.
https://www.reef2reef.com/threads/cyanobacteria-questions-answers-and-solution.253823/