100% water change is good on a 1 gallon bowl which is what it seems you have (Although 1 gallon is 3.8 liters, but that's besides the point)
In small bowls like that the ammonia will build up quickly, I'm sure you've read this already though. But that's good you're doing a change every other day. Are you making sure that the temperature of the new water is similar or the same to the old water?
Also, instead of aging water you can just get a conditioner such as Prime which is great for conditioner water so there is no ammonium from your tap, as well as heavy metals and chlorine (which is what you are getting rid of when you age your water) But with the conditioner you can add the water right away, take it from the tap, mix in a drop or two of Prime and add it to the bowl. But if you want to keep aging, that's fine as well :) What ever suits your fancy ^^
The clamped fins could be from discomfort of moving to a "new" home, as in new surroundings. If this is the case, just try not to bother him too much except for feedings and water changes which are crucial. Loud noises will also scare them, it might help him to get some sort of decoration. You'll have to make sure there are no sharp edges to hurt his fins though. If you get silk plants those are generally good for Betta's because they are soft.
To heal his fins, you will have to get a conditioner called Stress Coat (or Stress Coat +), it contains aloe which is very beneficial for your Betta to grow their fins back. It may take up to a month, but sometimes smaller tears can be healed at just a week! You use it like Prime conditioner, just take water from the tap (make sure it's similar in temperature) add in a few drops of Stress Coat and add it to the tank and this will help with his fins.
Also if they are stressed they may not eat but do not worry, I had a fish that wouldn't eat for the first month that I had him but now he eats like a pig! They can survive :)
Also I would cut back and only feed him twice a day and fast him for one day so he doesn't become constipated. Also live foods like that all the time isn't always good, especially in a small area. They can eat like that in the wild because they've got miles of water to swim around in and won't contaminate the water as fast.
I would look into getting some New Life Spectrum Betta Pellets or Omega One Betta Pellets, both of which have essential nutrients needed for Bettas. And then you could give him the live food many twice or three times a week. Generally you want to fast them after having a protein rich meal such as the live foods.
But that's great that he plays and his color is still vivid! I think that's all I can comment about for now...if I forgot something I'll just tag it on after haha. If anything doesn't make sense, please ask and I'll try to reword it to help! I hope the little guy can get better soon! :D
BTW, sorry for the long post >< I know it can be a lot to take in, sorry!