Neither name is derived from Latin. Rowling has suggested that she subconsciously named Hogwarts after the hogwort plant. "Diagon Alley" is a pun on "diagonally".
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In the Leaky Couldron, if you mean the bricks to enter Diagon Alley.
You can't Hogwarts is not a real place. If you mean the place where it is filmed there are many of them.
Do you mean after the Battle of Hogwarts? He is never mentioned as dead or even injured, so we can only assume he survives the Battle and continues teaching Charms at Hogwarts.
You mean what did he say instead of Diagon Alley. He said diagonally, and was sent to Knockturn Alley, luckily being rescued by Hagrid.
If by bad kids you mean Draco Malfoy and his friends, their jobs remain unknown.