If projecting on the moon is realistically very hard to achieve for an individual or a group of people, how would you project films on the night sky? One instance I was thinking was flying four drones and somehow keep them stable in one position with a huge screen tied to each corner of the screen and project on the screen. How would you achieve to project a film on the night sky? considering that audio for the film will be kept silent.
The projection of (moving) images on an arbitrary surface is trivial, it is done regularly.
Even if the surface moves a bit, that can be compensated for with a bit of computing.
So, the not-so-trivial job is getting the surface to where you want it.
Drones should be possible, but i guess you are aware that helicopter - or multicopter - style drones use massive amounts of energy to stay airborne. Your typical hobbyist drones can stay in the air for around 15 minutes before they run out of energy.
The large military drones like the predator and such are pretty much powered gliders (plus a lot of fancy extras), so they can stay aloft for much longer. But they cannot be stationary.
For a stationary object to stay aloft for a reasonable mount of time (say two hours) and pretty much stationary (so you don't have to run to be able to watch the movie) i would think about balloons or blimps. they don't need any energy to stay airborne, only to maneuver.
Whichever method you choose, they will all be extremely vulnerable to wind, for the simple reason that the projection surface is a very large sail.
So, on a calm day blimbs should be feasible, on a windy day even multicopters will have a hard time to stay stable enough.
Oh, and for the audio: you can simply send that over the web to the viewer's smartphone.
You don't want drones; you want femtosecond lasers. Just project into thin air.
Aerial Burton has used a plasma laser to float a 3D image in mid-air. At the moment it's very rudimentary stuff but it shows that light can be viewed without the need to bounce it off a surface. Until now any "hologram" examples have required glass, smoke or water to bounce light from. The Aerial Burton breakthrough creates light in the air.
So how is this possible without light bouncing back towards our eyes? The technology uses a 1kW infrared pulse laser which is focused on direct points in the air via a 3D scanner. At this stage the molecules in the air are ionised to create plasma. Since these plasma bursts only last a short while the laser needs to pulse in order to keep the area lit.
Alternatively, just screen your films on days with low cloud :)