You should backwash whenever pressure rises 25% over clean pressure- whenever that occurs. Sand filters actually filter better when they are a little dirty so backwashing too frequently isn’t helpful.
You should backwash until the water in the sight glass becomes clear- however long that takes. Then rinse until there’s no sand (maybe only a grain or two left) in the sight glass- however long that takes.
For reference, I have roughly the same size pool as you & a 250# sand filter & I have backwashed about 3 times since opening in early April.
The pump basket cleaning frequency depends upon how much debris you have. If you see leaves its time to empty it. You don’t want to starve your pump.
Right now it’s starting to be “leafy” out so I am having to check the skimmer & pump basket pretty much daily. During periods with few bugs & leaves I may dump the pump basket once a week.
As far as the chlorinator goes it should be adjustable whether the pump is off or on.
But Using trichlor pucks for daily chlorination will get you into trouble quickly. They add cya along with chlorine. The chlorine gets consumed daily but the cya remains in the water. As your cya increases so does the necessary minimum fc requirement
FC/CYA Levels. The only way to lower cya is to exchange water.
Pucks are also acidic so they lower ph & subsequently Ta so you must monitor all those parameters closely.
Before chlorinating your pool, you should know these simple tips. Learn the best way to add chlorine to your pool.
www.google.com
If you don’t already have one, you definitely need a proper test kit (taylor k2006 or tf100/pro) to manage your pool chemistry properly.
Test Kits Compared
Here’s a link to all the good info above in one place + more to help you care for your pool
Pool Care Basics