the second picture has what looks to be black edges, so that might be a little rot set in.
Make sure to keep the water cleaner while they have open wounds. Since it doesn't look terrible if there is any rot at all, just do a few more changes weekly to keep things pristine.
To discourage tail biting, try more decorations, stable light schedule, more opportunities to flare/exercise, varied diet, and interesting surroundings.
Plastic bottle caps make good toys and give you the chance to find out which color your betta prefers too. Or see if he wants to chase down something by tying a button to some string and dragging it around the tank. It'll float at first, but you can easily sink the button too.