Personally, I don't think PH nor alkalinity or temperature have much factor in S. haddoni's well being as long as they're within a reasonable range. I've kept S. haddoni in anywhere from 72-88 degrees without and visible signs of stress, the same goes for varying alkalinity and PH. In fact in nature I can guarantee you these animals go through some wild temperature fluctuations in addition to baking in the sun from time to time.
In short, don't worry about the temp dip you had and don't overly fixate on your parameters or if you're doing too few or not enough water changes... It's a new carpet anemone, they just need time to adapt. Sadly many carpets don't make it for long after being put in new surroundings, some do. I guarantee you many many of those anemones that didn't make it were in as close to ideal conditions as you'll find in home aquaria. Nowadays, assuming decent parameters, I thinks it's luck of the draw more than anything.
As for feeding, I'd personally wait, but if you want to feed it a little something I don't think it'll be harmful as long as it's something fairly small in particle size.
Their mouths are often a little more visible and open over night and before lights on, so your observations aren't anything out of the ordinary.
Lastly, from your last photos, you may not be out of the woods yet, but I can see a clearing
Good luck, it's a gorgeous anemone!