I am sorry I don't know what to tell you about the fin I hope it is okay, and your fishy is a cutie.
As for you questiona about the light and the bubbles I thought I could share with you that my betta was recently moved into a bigger tank with a air stone and LOVES the bubbles, he likes to swim through them playing like a young guy again

He did not like the bright white light from the new hood but when I tried some amber lights that are dimmer he did not seem to mind. the amber lights give a very unique coloring to his tank so I like it. He never had light before this new tank.
It probably depend on the fish though, if you add the light or the bubbles and your fishy seems disturbed by them you can always adjust or take them away, the good thing about bettas is that I find they are good at letting you know what they do not like

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Good luck with your new little one!