My knowledge of bettas and fin problems is essentially nonexistent, even tho I bred the darn things 3 decades ago! Bob really doesn't look all that bad to my eyes. You think he won't shape up after a couple more weeks/months of your love and attention?
Tank looks nice. Why do you keep the water level a little low? With a small tank and evaporation, I usually pay a little more attention to keeping water levels up.
Also, this is just my opinion, but I think the final photo - with the sveral larger rocks and two larger pieces of petrified wood - looks a little busy for my taste.
-I think the one piece of wood furthest on the right is a little too large - overpowering.
-And the number of large rocks pretty much eliminates the possibility of growing any foreground plants.
-I often find driftwood branches interesting in such tanks - adds curves and angles otherwise absent, creates tunnels and arches, while taking up little swimming room.
-Anarcharis is not one of my favorite plants - especially as a specimen in a small tank with only a few plant species. You may have a hard time maintaining it in a manner that complements the tank. May either get spindly, or overgrow the tank.
Hope this doesn't sound too negative. It really is a lovely tank. But with such small tanks, the smallest details can make a difference. And again, this is all just my opinion. (And, admittedly, the opinion of one who hasn't posted any photos of his own efforts!)