What is the make up of the "chlorinated pool shock"? (active ingredient) I'm wondering why you are shocking a pool that is in start up mode. You should not be running water through your system with a pH of 6.8 yet I don't see any additions of soda ash or bicarb to bring this pH up. That needs addressed now! You added enough chlorine to put 6ppm in the pool. That is pretty high for new work. 500 on hardness is high.

I'd suggest that your cloudiness might be from the excessive use of the stain and scale. Check for phosphates and remove if needed (the treatment will cloud the water) add soda ash to bring the pH up let the chlorine lower itself (pull the floater), make sure your filter is operating properly and add a clarifier. The best is Sea Klear PRS. It is a two stage product that will filter out the smallest of particles.

The obvious is how old is the plaster? New work will cloud for a week or so if you are brushing it.

Here's the good news: The cloudiness is almost certainly a by-product of your new plaster job. Nothing to worry about, just keep brushing 2 or 3 times a day and running your pump/filter 24x7 until it clears; probably about ten days.

Here's the bad news. Holy cow. I hope you made a typo. 12 gallons of 10% sodium hypochlorite (aka bleach, aka liquid chlorine, aka liquid sanitizer) will add about 57 ppm of free chlorine to a 21000 gallon pool. Yes, 57. That's a bunch of chlorine. What kind of chlorine test gave you 4 ppm? How long between when you added that chlorine and the test? Something is not right here. If it's really that high, the chlorine will come down on it's own eventually, but it will take some time (probably a week or more to drop below 10 ppm). If you need to lower it more quickly (i.e. if the plasterer has a cow), the only way I know of is with sodium thiosulfate; you can get that at a good camera shop that sells darkroom supplies. You'll need about 6 oz to lower your FC by 1 ppm. So, if your FC is actually still at 50 ppm, you'd need about 1.9 gallons of sodium thiosulfate to get to 10 ppm.

Acid will lower alkalinity but only in conjunction with pH. As your pH goes down the alkalinity will follow. When the pH rises again the alkalinity will go back up. I would not worry about alkalinity for the time being unless the plasterer is doing a high-acid start-up. If that's the case, he should be managing the alkalinity, not you. Otherwise, add about a pound of soda ash to raise your pH by 0.2 and worry about alkalinity after you have your chlorine, pH and calcium hardness in line.

I would NOT worry about phosphates. That is something to worry about when you've ruled everything else out.

I would not add a clarifier; especially when you have a new plaster job.