I'll let the great mods here handle the techy questions, but will just pipe in as a pool owner who has had to clear up the post-holiday green swamp effect a couple of times over the years.

It may take a while for the water will clear right up, longer than you may think it should. My my experience is the water is often cloudy for a while after all the green is gone and the chlorine readings look pretty darn good. I found that just keeping up the chlorine levels and waiting it out has worked, though sometimes that seems to take a couple more days than I think it should. I wouldn't get impatient and start tossing in clarifier or floc, etc. as it's just a matter of time. You are also killing a lot of organic matter, so the dead algae will accumulate in the bottom of the pool as a fine dust. Best to vacum that directly to "waste" or "drain". That will use water but is the way to get it out of the pool. I have a sand filter and a lot of the fine dead algae passes through it if I vacum it through the filter.

Hatching dragonflys is a new one though!