Does this year and model Hyundai have an EDR, Event Data Recorder?

To the best of my knowledge and from the information I was able to access, this vehicle does not have one. Hyundai did not start equipping their vehicles with them until 2013.

Are you referring to diagnostic fault codes? I'm more familiar with that on Chrysler products. They had that already in the early '90s, but it's nothing you can retrieve. Any diagnostic fault codes that are set can be erased by the mechanic after the repairs are completed, but a permanent record of those codes stays in the computer that only Chrysler can retrieve. They use that data to research potential emissions problems and to verify a problem really did occur in the past. They have that in their transmission computers too to prove a mechanic really did what was required when performing a warranty repair on a transmission. Anti-lock Brake Computers store data like vehicle speed and rate of deceleration just before a crash, but again, there isn't anything you can access.

All of the data available to you is erased when the battery is disconnected or the computer is removed from the vehicle.