doesn't לוח by itself mean "calendar"?
No - it means "board" or "table". But sometimes we can say לוח and mean לוח שנה, by way of abbreviation, if it is clear what we are talking about.
I was taught that לוח meant calendar. Probably another of my quaint antiquities. Never heard the term לוח שנה til now. We also used the word לוח to mean the blackboard or whiteboard in the classroom.
I wrote "אין לוח שנה לאף אחד" and it was marked wrong. Is there any reason this shouldn't be considered correct?
It just doesn't sound like correct Hebrew. This worked for me, though:
אין לאף אחד לוח שנה
Le’af ekhad ein luakh shana.
A question about the word order: you say:" אין לי ספר" so why is it :"לאפ אחד אין..." and not :"אין לוח שנה לאפ אחד"?