1. If you maintain the free chlorine at a high level it will oxidise the CYA slowly away. Using shock levels it would drop quicker but there is also a bacteria solution that will reduce the CYA level. I reduced the CYA from 200ppm down to 50ppm using high doses of chlorine which also helped burn out the quats and get back into control of the pool, the chlorine was cheaper than the empty/refill process.
2. The filter you have is tiny so it fills with debris quickly hence lots of backwashing. Those socks that go in the skimmer capture the larger particle the sand filter captures the small particles but as I just said yours is too small for the size of the pool, 20" or 24" would be better for that size of pump.
3 you would only need a tiny amount of DE for a filter that size, almost not worth doing, alternatives such as jolly jelly clarifyer work well but won't work that well in a small filter as they catch the dirt it's delicate jell gets pushed apart by the force of the water trying to blast through it. Gently is much better to catch things in the filter.