You seem to have some misconceptions on what chemicals do what.
Baking soda raises TA and pH only a little bit. This is in contrast with Soda Ash which raises pH a lot and TA only a little bit. So it's unlikely the baking soda is raising your pH because if it were, then you TA would have been increasing more than you're reporting.
Your chlorine tablets are made of Trichlor which is VERY acidic, so it would be lowering your pH, not increasing it.
Stablizier is CYA which is cyanuric acid. As the name suggest, it's an acid but it's in reality only a weak acid. Stabilizer would lower pH but because it's such a weak acid it's not going to have any effect on pH with just a few tablets in 28k gallons of water
Okay, now that we've gotten that out of the way, let's start with what's actually going on.
1. Running your pump and/or filtering is never ever ever ever going to fix your algae problem, algae is causing the cloudy water and what you're now seeing it's going green. You need to SLAM, nothing else to it.
2. Your pH rise is likely due to aeration, meaning your waterfall. Pool water has dissolved CO2 in it and as you aerate the water the CO2 leaves and pH rises
3. Your cheap walmart test kit is worth about what you paid for it. If you've been adding baking soda and your TA reading isn't rising, the reagents are probably just old, expired, and they are now junk.
4. Normally the pH test is good up to 10ppm free chlorine but that only applies to the Taylor pH reagent which uses chlorine neutralizers to make measurement up to 10ppm FC possible, we really don't know anything about HTH pH reagent. Your high pH reading of 8.2 could be falsely high because of high chlorine level (of course we have no clue what your chlorine levels are)
What to do:
1. I'd bring pH down a bit with muriatic acid, let's say 7.6
2. Add half gallon of liquid chlorine each day until you have a good test kit
3. Study the forum on SLAMing so your ready to go when you have your kit