Can I make the calendar completely read-only.
Yes. Administrators can designate individual users as having read-only access.
The read-only option can be set in the calendar settings under the group menu. From there, select the user account you'd like to set and click the yes/no radio button next to Read Only.
DayBack also respects your FileMaker Access privileges so you can control access there as well. More on that here: security.