I recently flagged a question on webapps.stackexchange.com and after around an hour received the Citizen Patrol badge. Does this means action has been taken against the question I flagged? - i.e., did it get closed/migrated or whatever was applicable?
No, receiving the badge does not have anything to do with the action performed by the moderator in response to your flag. You get the badge just for raising a moderator flag.
The only reason you didn't get the badge immediately after flagging is because the Automatic Badge Awarder script doesn't run constantly, because it's a relatively expensive process.
You can check to see if your flag has been processed, and if so how it was dismissed, by going to your profile and clicking the number next to the "helpful flags" text.
Not necessarily. The badge is awarded for flagging a post.
Badges are awarded by a recurring job, so there usually is a delay (up to a day or two) before you get a badge. This is normal.
If you want to check your flag status, go to your profile, click on the number next to "helpful flags". THis will show a list of all flags. Note that is a flag is marked as "helpful", the action was not necessarily carried out--"helpful" means that you flagged in good faith. Check the ost itself if you want to see if the action was carried out.