The tetra stuff is not good. It's one of the worst on wheat and fillers. The first two or three ingredients should be whole
fish. Fish meal just means fish bones and byproducts ground up. Sorry :(
Here's some general info on keeping bettas (it can all be found in the care forums btw)
Bettas need to be kept in 2 gallons minimum. In these twice weekly water changes of 50% and 100% are needed. Bettas kept in 1 gallon containers live an average of about 2 years compared to double that+ in larger containers. The 1 gallon would need 3 weekly water changes of 50%, 50% and 100%, and even then they will be subjected to ammonia.
Betta's also like wide shallow spaces, and need to breathe air. So really tall vases with next to no surface area at their narrow neck is not an appropriate keeping container
The 50% changes the betta can be kept in the bowl and use a turkey baster to remove half the water and as much of the debris as possible. For the 100% you need to remove him - scoop him out with a plastic solo type cup and set aside while you thoroughly rinse the bowl and gravel to remove the debris. Then he should be acclimated to the new water by floating for an hour while you slowly add a couple tablespoons of new water to the cup every 10 minutes. When you release him, try to let as little of the old cup water back into the tank as possible. All water changes should use same temp water, matched to running tap using the in tank thermometer and the water needs to be premixed with conditioner before adding it to the betta tank. If you don't already have anything, you can use gallon water jugs from the grocery store - rinsed thoroughly in hot water but no chems.
Bettas are tropical fish and must be kept at a temp between 76-82, with 78-80 being ideal. The temp must be stable and not be dipping or jumping around. In a 2 gallon you can get an adjustable 25w heater. Any new heater should be tested for 24 hours in similar size container with in tank thermometer to make sure it will hold a constant appropriate temp between 78-80F. Then the betta must be acclimated to higher temp either by floating in a cup inside the main already fully heated tank for an hour, or by adjusting the heater to increase the temperature of the tank no more than a degree per hour and 5 degrees per day.
You should look for a good quality pellets whose first two or three ingredients are whole fish, not fish meal or wheat. He should be fed two small meals a day (how many depends on the pellet you pick up) and one fast day a week. Blood worms should be fed no more than one once a week as a treat in replace of pellet meal. Anything freeze dried needs to be thoroughly soaked in separate cup with some tank/treated water for at least 10minutes before feeding.