The door never existed before Lucy killed Alicia and left her room. Undetectable ninja's went in with building materials, build a brand-new door before anyone else could notice, then left.
Lucy never jumped off Alicia's window. She just fell so she landed safely.
Alicia was killed once, was REVIVED by her murderer in that room, then died again later when the murderer was not in the room and everything was closed by Alicia.