How we cite our quotes: All quotations are from Harry Potter and the Prisoner of Azkaban.
Quote #4
MCGONAGALL: Sirius Black was, and remains to this day, Harry Potter's godfather!
Harry's family tree gets complicated when he discovers that Sirius Black is his godfather. Of course they're not related by blood, but Sirius is the closest thing to a parent that he has. It's alarming for him to discover that he might be even worse than the Dursleys.
Quote #5
HARRY: I was thinking of him. And Mum. Seeing their faces. They were talking to me. Just talking. That's the memory I chose. I don't even know if it's real. But it's the best I have.
Harry must think of a happy memory to conjure a Patronus, so of course he thinks of his family. These tiny memories of his parents keep Harry going in dark times, and the more he thinks of them, the more real they seem to him. He'll never forget them.
Quote #6
SNAPE: How extraordinarily like your father you are, Potter. He, too, was exceedingly arrogant, strutting about the castle.
Lupin already said that Harry is very similar to his father. That's why Snape dislikes Harry, because of that similarity. Snape was always jealous of James, and Harry reminds him of his own insecurity.