WaterWizard said:
In all my treatments of algae (which is well over 10,000 water test's) You have three things to start Chemistry, Brushing, And filtration. When one fails we get algae.
You are past the stages of shocking "white algae" is dead algae, you should be vacuuming and back washing(until sight glass is clean). while not vacuuming I would keep the suction to your main drain. If water stays cloudy you can use a clarifier like ultra bright.(they have tons of options for the product this one is just on the top of my head).
Remember once clean and looking good, test once a week and keep it balanced, brush the whole pool once a week and circulate the pool 10-12 hours (summertime) 4-6 hours (wintertime).
of course check baskets frequently.
Welcome to TFP!!!
Just to address a few of your points:
Chlorine is really the most important thing required to avoid algae ... and some circulation. You could have no filter and maintain the FC level and there would be no living algae.
We also generally do not recommend and clarifier / floc products until a last resort. Sometimes they work and sometimes they make more problems. If the filter is working correctly, the water will clear (a little DE can help the sand filters speed this along).
Our general recommendation is to backwash the filter when the pressure rises 20-25% above the clean pressure ... do this long enough so that the water is clear as you state. Additionally inspecting and cleaning the sand once a year can help settle the sand.
Finally, there is no real right answer as far as how much to run the pump. You really just need to run it long enough that the water looks clean enough to you. But generally, the winter time run can be much shorter than in the summer as was stated.