I tend to be a paranoid person when it comes to my children's safety. My worst fear is either of these liquids creating a pocket or saturated area that someone swims through and has irreversible eye damage (or something else equally nasty).
1) I guess the best way to look at this is, what exactly happens to either bleach/Liquid Chlorine or muriatic acid when added to pool water if, say, the pump was off? If these chemicals are denser than the water, do they sort of sit in pockets in the area you added them to? Would they sink slowly in a concentrated clumps, or does it naturally spread out evenly, yet slowly, over time? Does it spread out over the walls?
2) Is it better to pour slowly in the deep end near a return jet, or pour evenly around the entire pool OR pre-mix it in a bucket and THEN pour evenly around the entire pool? The issue with the first seems to be possibly creating dangerous pockets that can hang around or saturated areas that take longer to mix evenly, and the issue with the second/third is it's more of a pain in the butt as well as splashing on you and the decking (really an issue with muriatic acid).
3) I've heard also that brushing the walls (whole pool or just deep end?) after you add is recommended, but why?
4) How long, with the pump running, can you safely expect these chemicals to be evenly mixed in the water, and does size of pool and pump P.S.I./water turnover rate factor into that? I have a fairly large pool of 30,000-35,000 gallons and an energy efficient variable speed pump that I am currently running at about 10-12 p.s.i. on a 500 lb sand filter.