Unless there is some type of glitch going on, if you have a Search for Interviewer function, you have an invite! (99% sure). The automated emails usually get sent out a little after the update has been made to your application, so it shows up after a login before you get the email; at least that is my experience after two years of applications.
As far as the interview advice: IMO "Why Columbia" is key. They might only ask you it once, but you can answer it with almost every question. Make sure to weave in clubs/classes/professors/conferences you're interested in. I interviewed last year and this, and both were laid back, with standard behavioral questions (walk me through your resume, why mba, why CBS, describe a leadership situation, etc), so just know your resume, have your clear goals and try to have Why CBS come through crystal clear. Good luck everyone!