I want to set up a section of the forum where a moderator or admin posts a new thread and registered users can only reply to that thread, they cannot post a new thread. Is there a way to do this?

This can be done with the access mask Admin -> Users and Roles - > Access Masks There is a Flag for Reply Access and Post Access. You need to uncheck Post Access.

No you can assign this Mask as Member Access Mask to any Forum you want.