Hi @Somnambulik1 ! Of course you can play videos in Unreal and yes Unreal prefers mp4 files.
Here is the recipe:
you will need a media player:
when you create it you will be prompted to create a media player output texture asset…mark it and create one too:
Of course you need an mp4 to play 
put the mp4 in the contents folder of the project inside a folder called MOVIES (is important to be there and the folder to be named MOVIES)
also add a media source:
open media source and select your movie:
…save and close.
create a material:
define the material as USER INTERFACE:
main node will look like this:
add a texture sample and connect it to final color:
as texture select your media texture:
save the material and close
create a Widget blueprint
open the widget and drag and drop an image component:
select the image and choose this anchor type:
put all this values in 0:
your image should take the whole widget like this:
now put the material in the brush slot of the image:
save the widget and close
open the level blueprint
create a media player variable. press compile and then assign the media player you created:
now you must create an instance of your widget and put it in the screen. then use your media player variable to open the source media and play it.
play the project and enjoy the movie!
P.S.- Before you ask it: in windows you wont hear anything from the video. in this case you must have the audio as audio component and play at the same time.
in other platforms (like android), the audio of the mp4 file works fine
