Do any airplanes really have this piece Tom Cruise is hanging onto in this movie?
The plane is an Airbus A400M Atlas, a four-engine turboprop military transport aircraft.

I'm referring to this page, and there the stunt is well described.
About the door, here's an explanation:


  Visible in the released image, the A400M's new side door deflectors were added to the development aircraft fleet after initial tests with the ramp and side doors open resulted in high noise levels and turbulence inside the cargo hold, says Fernando Alonso, Airbus Military's senior vice-president flight and integration test centre.