This is referring to the core joomla images directory. You may or may not already see /dtregister in that /images folder.
Also when I create a new course it is already close - no ability to register. Must be doing something 'really basic' wrong.
Yes, you most likely have set the "Start Date" for the actual date of the event. This is when registration opens... not when the event starts. The event dates come from JEvents and are not setup in duplicate in DT Register.