I like frozen blood worms . I just started recently feeding all my bettas with it. I had my 3.5 y old betta got bad fin rot about 5 month ago . I really think that frozen food helped his recovery , of course along with medications. So since that i feed them once a wk , or once every 2 wks. I am lazy
But i feed them a few different kinds of pellets , dried daphnia , dried blw. Frozen food a little messy so i feed them the day when i do full water changes. For you just give one blood worm at the time. You can use a tweezers to feed. Just be careful , hold one end of the blood worm so the fish don't touch it and hurt the lips.
10 gall do minimum 50% weekly with gravel vacuuming, filter media swish/rinse in the tank water weekly to get rid all that gunk that gathering on them regularly.It more important to do that , then change the cartridge . You don't have to change it a lot just rinse it. Check the water parameters and do additional water changes if needed. Its always good idea to do extra water changes a wk though. Test kit don't show how much bacteria in the water from all that waste that fish produce.
Do not put betta fix or any medications with ''fix'' in it. I would return it. Its has tea tree oil and can damage betta's labyrinth organs. If it tail biting or even injury from the filter he should be fine with clean water. May be do more water changes, 2-50 a week. Go return bettafix if you can or exchange it for a stress coat. Stress coat has Aloe Vera in it and helps with the healing. Sometimes biting is difficult and fish can do it regularly , so all you can do is keep the water super clean to prevent an infection and stress coat. But you need to make sure he will not develop any discolorations on the tips of his tail.