Okay for a 2 gallon tank, water changes are best to be 50% and 100% a week. That is what I do for Cheshire's 2 gallon tank
The water pre-treat with conditioner a day before the water change and let it sit for 24h.
Keep the temperature stable, you might want to get a thermometre, they are 1-2$ in dollar stores, and in wallmart I think for a mini. If not in the u-s they sell them cheap in local pet stores.
Also, and please do not be offended, but I think you feed too much, 8 pellets a day is a handful. I recommend feeding your betta 4 pellets a day, my betta's get fed 2 pellets in the morning and 2 at night. With 1 day of fasting for digestion a week, and on fridays they get fed dried bloodworms or frozen brine shrimp.
Bettas won't starve for a day of fasting, in fact most betta's get into health problems due to overfeeding. They dirty the water more as well.
If you still want to feed them 8 pellets regardless, pull out uneaten food so it will not rot in the tank.
Also to help healing of the fins and reduce stress, use an indian almond leaf or oak leaf which will release tannins that will help avoid infection in the injuries and relax the fish. (It will dye the water brown a little)
Api stress coat is also good as it contains aloe vera that helps with the healing process.
Also keep an eye on him, avoid bright lights and anything that can stress him out.
While injured just make sure to keep his water extra clean to avoid infection.
good luck and keep us posted :)