Your doing great ciaka. I would just caution you to not let your FC drop like that. You really don't want an algae outbreak right now, in a new pool. Don't let it drop below 3. Test more, add more, whatever you need to do. 3 should be your
minimum right now, not the max. If you slip up and it falls to 0, you don't take days to get back to 2.5 or 3, you add enough chlorine right then and there to immediately bring your FC to 3 or more. Algae can grab hold really quick, so don't lollygag when it's below 3. (That's right, I said lollygag!

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As Allen points out, CC of 0.5 is just fine. CC is a byproduct of the chlorine gobbling up the nasties. It's what's left over after the chlorine does it's thing. Kinda like a picked-clean carcass. To see 0.5 every once in a while just means some nasties tried an assault and lost. To see a CC of 1.0 or more means the nasties are starting to win! CC will come and go, so only worry about it when it climbs higher than 1.0.
Fun fact: remember the last time you were at a public pool and smelled chlorine? That wasn't chlorine. What you were smelling was CC. Which means if you can smell that, then the chlorine is working that hard to produce that much CC, which means what? Yep, there's that much nasty in that pool! Yuck. The bummer about the TFP method is: once you get your pool dialed in, and learn what a truly clean and sanitized pool feels, looks and smells like, you'll never be able to swim in a public or hotel pool again!! Oh well.
The lower you take your pH, the faster it'll come right back up. That's OK, and expected. By lowering your pH the way you are it's also lowering your TA, which is good. So stay the course there. Once you get your TA down doing that, you'll see your pH stabilize and then you can be less aggressive about lowering pH. But for now, you're good. Your pool is curing right now and needs a lot of acid. Totally normal. The longer it cures, the less you'll need, but you'll never get down to none. You'll always be adding acid to your pool, but in time it'll be much less than now.