I agree with aylad, everything about your intex is real; the wetness and the responsibilities. Some people seem to think these pools are toys (I bought my first one in a toy store) which never works well. FWIW I found my Intex donuts harder to maintain than my traditional AGP. With less water and poor filtration, things can go south in a hurry.

You seem to be heading in the right direction (and you're in the right place to learn) as far as maintenance and chemistry but I haven't seen yet where you've ordered the K-2006 aylad recommended. My opinion: it is the single most important start-up chemical for a new pool.

I've never see a through-the-wall skimmer for soft side pools and can't imagine how it would work. As far as additional returns: I wouldn't want to cut the pool and the one should be OK for a 15' pool. If you have the time and don't mind the back-breaking work, I supppose putting it in a hole could work, I just don't see why. You'd need to modify the ladder. Does your pool have the rope that goes around the bottom of the legs to hold them upright?

There are pump / filter choices in the Intex world (all cost more than a K-2006), sand and cartridge. Ben has made some recommendations for filter cartridge upgrades that you may want ot consider in the Construction, Equipment, Operations, Seasonal Care (P)Intex-type Pool Setup & Operations section of the forum. There's probably a lot of stuff in there you want to read anyway.

Good luck and have fun!