Is there a ticket box office at memorial hall to purchase a ticket before the show?

Depends on the event. They usually have a table for taking people's tickets. Always good to view the event page or call

I have only attended Cincinnati World Cinema there. They set up their own box office and it implies to me that it's up to each organizing event whether there will be a box office or not.

Yes.

For the shows that i have attended there was a box office for will call tickets. Presumably tickets could be purchased there.

I think it depends on the show, but the general answer is yes.