Black and brown spots on the leaves, most of the time it mean deficiency in minerals and other nutrients. If it is indeed black spot algae, it is something completely different. Lights not strong enough can cause plants become weak too.
I wouldn't jump onto UV equipment. A long time ago I almost bought it myself to treat both algae and parasites, but I stopped my urge and I am not missing it. Just another piece of non-mandatory equipment to burn your money with. There are many ways to control algae at the source, including limit the time of the lights exposure to even fewer hours, and keep the organic waste low by doing partial water changes.
Before you buy more substrate, mix them first to see if the situation improve. Sometimes the fish do not like the reflected light from lighter color substrate from what I have heard.
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20 gal tank - good mix of community fish ?
There are many ways to control algae at the source, including limit the time of the lights exposure to even fewer hours, and keep the organic waste low by doing partial water changes. 
