You need at least 2 gallons to keep him healthy long term and even that will take 2 water changes a week - one 50% and one 100%. The 100% should include a thorough rinsing of all ornaments and especially gravel to remove all poo.
I would also not use flakes and stick to pellets and supplement blood worms only once a week - make sure none sink to the bottom and fish them out if they do. Flakes muck up the water a lot faster, and you just can't help but some of it getting dissolved or falling in ways you can't retrieve in there. Also make sure he's getting one fast day a week.
For now, do 100% daily water changes in that.
Bettas are usually approx 6 months old when you get them from the pet store. Their age is that plus how long you've had them.
You can do water changes like this to avoid shock:
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.
Since your house temp is warm and you don't need a heater you can also premix gallon jugs or buckets or whatever with his water and let it sit in the same room as him for 24 hours. That will also equalize temps.