You absolutely need to be using a conditioner with the water, and with every change. It should be a liquid and it should say it removes chlorine, choramines and heavy metals - make sure it says all three. Tap water is toxic to bettas without it.
In a tank/bowl of this size two water changes a week are needed.. 50% and 100%. He should be scooped in a little plastic solo type cup and not use a net. New water should be the exact same temp as old water - matched using his in tank thermometer. Water and conditioner should also be premixed (you can use fresh water jugs from the grocery store - rinsed well in hot water but not chems).
He is also freezing at that temp, and the swings are hard on him. They can even be lethal. What heater are you using? It's not working properly. You need one that can keep a constant unchanging temp between 78-80F. With a tank this size you can get a 25w adjustable heater. Make sure any heater you get is tested 24hours in similar size container to make sure it will maintain a constant appropriate temp. You must always use an in tank thermometer to monitor the temp. He must be acclimated to the water water either by floating in a cup inside the already fully warmed water for a hour, or by adjusting the heater to increase no more than 1 degree per hour and 5 degrees per day.
He should be getting two small meals a day, at least a couple at a time and one fast day a week. You should look for a pellet whose first two or three ingredients are whole fish and not fish meal or wheat. How many you feed depends on the pellet you choose.