With regards to 1?, those are table alias names.
Do you see the FROM user_stats st line? That’s telling the query that st is short for the user_stats table
The same is true in JOIN statement where it says users u. It is saying that in query u is an alias for the users table in that query. Aliases are used to allow simplifying queries to use less typing which reduces the chances of errors.
With regards to 3, if you enable that option then if a user no longer qualifies for a badge based on the query it will remove the badge from their account.