Yipes! Ted is the guy on DE.
I thought it wasn't a cartridge because you have a multi-valve on the side. They are not common on cartridges. Most of the junk (yes, it's junk) from the pool store shouldn't be used. If you can return it, do so. I'd keep the DE and the liquid pool shock, but ONLY if it's sodium hypochlorite. If it's "non-chlorine" get rid of it.

Phosphate remover is the latest junk chemistry the pool companies are pushing. If THAT is your problem you have far worse problems. I don't know anyone who has actually needed that stuff--PoolDoc MAY have, and Waste and Waterbear could as well...maybe.

Not sure what the "blast box" is but I'm guessing it's packets of Cal-hypo or Di-Chlor. If so, you can use those, too.

What is the horsepower on the pump? And how many gallons is the pool?