Much of what you ask about is covered in the SS recipe, if not fully explained.

The Best Guess page (linked in my signature block -- SS recipe link there, too) explains how you can have high chlorine and STILL have algae. Please note that the SS recipe applies ONLY to freshly filled pools. To use it, you'll need to drain and refill. Otherwise, you'll need to get a Taylor K2006 kit from Amazon (link, again), so you can measure and manage high CYA and chlorine levels.

The filter issue is covered on the SS page, and their are links there to cartridges that will both save you money AND perform better. But no matter what you do, the Intex pools have undersized pumps and filters, so you have to completely avoid algae to maintain good water quality.

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