If I change the 24 hour calendar halfway through the project, does it affect the other tasks timing?
This will affect the entire project. You can also set only just for some tasks another calendar by going to Task information dialog and in Advanced tab set the desired Calendar. By default, the Calendar is set to None so the task start and finish dates are calculated using the Project Calendar.
Note that these changes will not affect the completed tasks (100% complete) from your project.