Did the sorting hat make a mistake with Snape?

No. Nobody has been wrongly sorted, because the Hat makes no mistakes. The fact that Snape was ‘brave’ means little; Dumbledore was unarguably the most brilliant character, yet he was a Gryffindor, not a Ravenclaw, and so was Hermione.

Why was Harry almost put in Slytherin?

It suggested that Harry would have great fame and glory by joining Slytherin House, as Harry possessed Slytherin qualities such as cunning and determination.

What would have happened if Snape was never sorted into Slytherin?

Should Snape have never been sorted into Slytherin, he wouldn’t have spent nearly as much time with the wrong sort of people, he wouldn’t have received James and Sirius’ disdain, and his friendship with Lily wouldn’t have abruptly ended. Lily’s good influence on Snape was now lost. Maybe Lily and James wouldn’t have got together.

What happened to Severus Snape and Lily Potter?

The pair were parted when the Sorting Hat placed Severus in Slytherin and Lily in Gryffindor, and while Lily thrived in her new, magical life, Snape was essentially placed in close quarters with the likes of Lucius Malfoy, Avery and Mulciber. Mulciber!

What happened to Lily and Snape when they went to Hogwarts?

But when they went to Hogwarts, everything changed. The pair were parted when the Sorting Hat placed Severus in Slytherin and Lily in Gryffindor, and while Lily thrived in her new, magical life, Snape was essentially placed in close quarters with the likes of Lucius Malfoy, Avery and Mulciber. Mulciber!

Why was Harry so sure about himself being a Slytherin?

He was so sure about himself being a Slytherin because his heart wanted it. He got into a fight with James just because he overheard him talking smack about Slytherin. He had all the positive qualities of Slytherin like ambitious,shrewd,cunning and self preservation.