Hi beddini. I was asked to take a look at your thread and see if there was anything else I could add. However, I think OFL has you pretty well-covered on the treatment side. I agree wholeheartedly with her that this is definitely not velvet. Not sign at all of the characteristic gold flecks.
I agree that this may be aging. Since a betta's average lifespan is 1-3 years old and a betta can be anywhere from 3-12 months old by the time they reach the pet stores, it's possible your betta is even older than 2 years.
Have you noticed any abnormalities with his, er, poo? Any white stringy poo? He's a bit thin despite getting a proper diet and this can be caused by either old age itself or possibly internal parasites such as tapeworms. If you haven't seen any abnormal poo, it's probably safe to say this is old age at work.
To answer some of your questions:
Temp swings between 77-81 are probably okay as long as the swings are gradual, such as natural cooling and heating periods that you might see in the wild. If the swings are rapid like they go from 77 to 81 in the course of an hour or less, then there's a problem.
Your GH. I haven't had any problems using my GH kit but then, my water is like uber soft because of a water softener. My guess is that your GH is probably fairly high but your KH is, as noted, extremely low. Crushed coral will help to stabilize your KH. Add it to your filter (use a filter media bag if you can) and start out with a relatively small amount, increasing as needed. Don't use the pH uppers/downers as those won't help.
To prevent some of the most rapid pH swings, it will help to "age" your water. Fill up a bucket (add a heater if necessary to keep the water from getting below 75 or so), add your dechlorinator, and then just let the water sit for at least 24 hours. This allows the pH time to adjust itself and settle on a number without shocking or stressing your betta.
For your carbon: don't worry about it. :) As Ayala said, unless you're trying to get rid of toxins or meds, carbon does little else but keep the water clear and odor-free. Just leave what little carbon you have left in there. If you find you do need to replace it and/or the mechanical filtration, try leaving the old filter insert in behind the new one for a few days and monitor for ammonia swings.
By the way, IAL does soften water so if you plan on aging your water, it might be best to add the IAL then so it can factor into the pH swings.