Ciao Cristina, 'The curtain hung across' means that the curtain is covering the open door into the next room, in order to enter you have to push the curtain to one side. We use hang to describe how things are attached to other things. For example doors are hung on hinges, pictures are hung on walls, lights can be hung from the ceiling. Curtains are hung across doors and windows. A bucket hangs on the end of a rope down a well. You can also say 'suspended' or 'attached', but hang works really well as a description.

The curtain hangs across the open door into the bar. You need to use the preposition. In this sentence, ‘hangs across’ indicates that the curtain goes from one side of the door to the other. It spans the doorway. ‘The curtain hangs in the open door into the bar’ means almost the same thing but doesn’t indicate that the curtain spans the doorway. In this case, it could span the doorway or be only on one side of the doorway.