I'm not sure about the gills, but betta's can shred their own tails by biting them.
My Apollo did a round on his, it looked like he took it through a paper shredder. Some say biting can only look like hunks taken out of their tail, but I witnessed him in the act taking it apart like a cheese string.
I don't think anyone knows the real reasons they bite their tail, but some believe it is because they are bored...or maybe stressed. I took it that mine was bored and tried to fix some things -- his tail is healing nicely right now.
Does he have anything to explore in his tank? Like a cave?
Do you rearrange his décor once and awhile?
Is he in a high traffic room where he has some human interaction?
Is he nearby another betta where he can see it all the time, causing him stress?
Can he see his reflection constantly, causing him stress?
You said the tank is heated but what temperature is it at? (stick a meat thermometer in it if you don't have an aquarium one)
Tail biting can be a pain, mine stopped after a day once I rearranged his tank and gave him some taller plants to maneuver through, it sounds like your tank is on the smaller side though, so I'm not sure how much you can change.
I also took someone's advice and rearranged things outside of the tank too to give him different things to look at when I'm not home. (These fish are such babies sometimes, haha)
Have you looked at the oldfishlady water change schedule sticky under the "habitats and accessories" forum?
I would first ensure the water change schedule you have is accurate for the size of tank to make sure his tail will stay healthy. Regrowth will happen on it's own, but you want to make sure he has clean water (following the schedule) to make sure the bitten ends don't get infected with fin rot.
If his water is clean it will start to mend (you'll see clear regrowth)
But I would think if the reason is boredom or stress, and then pick one thing you think will help, and then reassess after a couple days.
You said "for now" when mentioning he had enough room, are you thinking of upgrading him in the future?
