I'm assuming you're using test strips for testing? The test strips are generally unreliable--that's why we recommend that pool owners who want to control their own pool water get a drop-based test kit.

To know whether the "dirt" stuff on the floor is algae or dirt, you need a way to measure chlorine at night and then again the next morning to see if you've used any chlorine during non-sunlight hours. You can't do this accurately with strips. In a windy climate, I'm guessing it's probably dirt or dust, but with a CYA at 30-50, and a FC at 3 ppm, which is on the very lowest edge of the acceptable chlorine range for that CYA level, you could have some algae trying to start up.

You only need to add stabilizer if you're experiencing an increase in chlorine consumption and have eliminated algae as the cause. As your CYA levels increase, so must your chlorine levels, so keep that in mind.

Stabilizer does take several days to register, so there's no need to test for it for at least 3-5 days (if using the powdered type). For everything else, assuming it's added into the return stream where water comes back into your pool from the pump, I would recommend waiting at least 10-15 minutes between additions of different chems to give them a chance to be dispersed well in the water.