I'm not sure exactly, but there could be a young protagonist who discovers the black unicorn. This character might be on a journey of self - discovery through their encounters with the unicorn.
Obviously, the last unicorn herself is a very popular character. She is the center of most stories, with her grace and magical nature being the main draw.
The main character is, of course, the last unicorn. There is also Schmendrick the Magician who plays an important role in the unicorn's journey. And Molly Grue, who has her own story and connection to the unicorn.
Since I don't know the exact Unicorn Wars story, it could be that the main characters are different types of unicorns. Maybe there's a brave young unicorn who is the protagonist.
There could be a young hero or heroine who tries to either tame the dark unicorn or understand it. This character might be on a quest for knowledge or power and sees the unicorn as a key part of that journey.
Obviously, Harry is one of the main characters. Since it's about him healing the unicorn. The unicorn itself can also be considered a main character as the story revolves around it. There might also be other characters like Hagrid. Hagrid could be the one who tells Harry about the injured unicorn in the first place, or he could assist Harry in some way during the healing process.
Yes, there might be. Given the fantastical nature of the novel, it's quite possible that there are characters or creatures with flaming eyes to add to the magical and mysterious atmosphere.