First of all, for a well stocked tank and no live plants, I would change at least 30% a week. With live plants it can be less because the plants will use some nitrate as fertiliser. But a lot of nitrate is not good for fish, and in the absence of live plants, water changes are the best way to remove the nitrate made by the nitrogen cycle.
As a rough guide, you should keep your nitrate level less than the amount in your tap water plus 20. It will be highest just before a water change, so this is the time to check your reading.
I have never used nitrate removing media so I'm afraid I can't help with that. I am lucky that my tap water has under 5 ppm nitrate so it is easy for me to keep my nitrate low.
When I had gravel, at every water change I used the gravel siphon to suck the debris out of the gravel. I moved decor to one side to 'hoover' under it. With no plants growing in the substrate, the muck (fish poo, uneaten food) will just sit there unless you suck it out.
I never bleach any decor. The simplest way to remove algae is to buy a cheap toothbrush and just scrub the rock or whatever in old tank water.
However, you can try to stop the algae growing in the first place. Keeping your nitrate level low will help, as will not having the lights on very long. How long are they on for at the moment?
Another way to help with algae is by having live plants. You don't need to get a jungle, but some floating plants would help enormously. These float - obviously - and are near the lights so they don't need anything fancy. They are on the surface so they can absorb carbon dioxide from the air so you don't need to add that. And fish like to have a shaded area in the tank. Look at Salvinia for small plants or water lettuce and Amazon frogbit for larger plants. Even duckweed would help.
As for checking levels in the tank, maybe check ammonia and nitrite after each water change for a few weeks to be sure they stay at zero, then test whenever you feel like it.
I would test nitrate before and half an hour after each water change for a while. And test your tap water so you know what the nitrate in the new water is.
The amount in the tap water will give you a base line to work from. If the tank nitrate just before a water change is more than 20 higher than the tap reading, you need to do a big (and I mean big) water change. If the after water change nitrate is still 10 or more above tap water level, you need to do another water change because in a week it will get higher still, probably back over tap + 20.