Do planes use autopilot when flying in formation?
Nope, pilots do not use autopilot to fly in formation. An autopilot cannot achieve the precision required for flying formation (e.g. keep the wingtip aligned to that door). Usage of autopilot would also hinder responses when an immediate correction is necessary.

You may refer to the TV episode Jet Stream and Blue Angle training videos on the internet. From the pilot's perspective, the planes are always moving around, though in a confined space. Continuous small adjustment is necessary. From the ground, the small floating cannot be noticed visually because the observer is too far away.



P.S. Based on my 17 years of experience with PC flight simulator, flying in formation in multiplayer is definitely doable, and can become second nature with practice.