Well, both of those pics look like fin rot to me. Black around the edges, or red (blood). But fin rot kind of looks like if you were to take a piece of paper or something and burn the edges. Being bitten looks like you just cut them off with scissors.
The fish is probably getting picked on by the other ones. Most fish will set up a pecking order to find out who's boss, just like other animals. There will usually always be a leader.
If I were you, I would quarantine the fish by himself to heal, and do water changes often to make sure it doesn't get a bacterial or fungal infection.