Unless you have past employers stating that you were a bad employee, or references stating you're a shaddy character, you have nothing to worry about.  I passed, and I left two jobs with no notice given.  The FBI understands that those things are gonna happen.  It's BIG things that will fail you on the background.  By the way, expect the background to take about a month or so.  If you traveled out of the country often it could take up to 3 months.  Good luck.

Maybe a month.  Usually after they finish the background they will notify you of your Quantico date.  Your spouce, if you have one, is the last person they will talk with on the background.   If you completed your medical exam and you haven't heard anything on it, you can assume there isn't anything you need to clear up and all went well.  So generally about a month until you go to Quantico.  While in Quantico you will find out where you're first office will be located and you will be given time to search for housing, and when you find something you can start the process of selling your current place and moving your family.