Betta Fish: New betta owner pls give advice !!

I was given this betta and he lived a small bowl for a while (I'm a minor and my mom insisted a bowl was fine😞) until I saved up and got him a 5 gal tank !! I got Topfin's 5 gal starter kit that came with a filter (Topfin's hang on back filer), thermometer and a lid with a white led light, which I think is too bright but Idk. I also got him a heater (also from topfin, it's set at 78°, I'm gonna get a better, adjustable heater eventually !) I think I did a pretty decent job setting up his tank but I didnt actually cycle the tank properly before putting him in :(( I tried to do a fish in cycle and I think the parameters look pretty good (they're shown below) !! Pls tell me what I can do to improve them. I also wanted to know about what filter media I should use bc rn I m using the filter cartridge that came with the filter and i heard those arent great but I dont rlly know what to replace it with, also I'm a little worried about his fins, I think he has some minor finrot so I'd love to know how to help him with that ! Sorry this is long but advice is much appreciated !!!