I wouldn't like to make things too hard, so I'm explaining some things, changing others, and using your feedback for this.
Jack: a sheikah that was raised outside of Hyrule. He often goes to the town to steal food and money. He's a wanted criminal. He's somewhat stubborn, and he will never let himself lose, even when he's defeated, what sometimes help him on fighting.
Guillermo: Guillermo is a close friend to Jack since they met and had a sword fight for reasons not-well explained (it's always confusing the story of how they met). He tries to make Jack see that he's wrong, what leads them to a constant fight.
Catherine: a gerudo born in the gerudo desert, but didn't like how the Gerudo had to live, and they were kicked out of Hyrules, so she decided to change things. She wants peace between the two races. She joined Jack's gang for unknown reasons.