He looks like he has a very white head and belly via the photos.. is this true? is it fuzzy at all? Does it looks like he's missing scales?
Light needs to go out at night. He needs darkness to sleep just like you do.
If you're using the light to heat his tank this isn't an appropriate method. It will cause swings. You need a proper heater and an in tank thermometer to monitor it. Any heater should have a thorough test run for 24 hours in similar sized container to make sure it will heat to a proper temp and hold it there (no swings). And your betta will need to be acclimated to the hotter water slowly.
You need to increase water changes. In something that small he will always be exposed to low levels of ammonia and there's not much you can do about it. That's one of the reasons why 2 gallons is considered minimum to keep betta's long term. In what you have 2 water changes a week are needed at minimum - one 50% and one 100% which should include a thorough rinsing of the gravel and all decor.
Your feeding is on the high end. Make sure he's pooping regularly and not looking bloated. If he's not pooping regularly and looking bloated you could cut back to 2 2x a day. No matter what or how much you feed he needs one fast day a week with no food.
Here is how to do all those water changes without shocking:
To do a water change, use a little cup like a plastic solo cup - this cup must be only for him and have never been used with soap or other chems. Scoop him up in this cup (keep him in the cup about 1/4 full of water - it doesn't need to be much because he won't be in it for long) and leave him in the cup while you change his water. To do the 50% use a turkey baster - dedicated only to him that has never seen soap or chems - and drag it through the gravel and try to suck as much of the poop out as possible, in addition to 50% of the water. Use a thermometer under the running tap to get it to be the same temp as the water that is normally in his tank. When the thermometer says the flowing tap is the right temp, fill back up his tank. At this point, add the conditioner (dose for how much water you change - if you change half the water you add half gallon worth of conditioner, If you do a 100% water change dose for the full gallon change). Float his plastic cup with him in it in the new water. Slowly add a couple tablespoons of the new water into his cup every 10 minutes for at least an hour. Finally, dump him in gently but try to get as little of the old cup water back into the tank as possible. When you do the weekly 100% you will do mostly the same thing except empty his tank fully and rinse everything in it very well under warm water but never use soaps or chemicals. Once it's fully cleaned/rinsed you can refill it and repeat the cup/acclimate phase.