Advice needed

I have several text fields that have associated checkbox fields. When user fills out a text field the associated checkbox text field should get checked. On the other hand when the user empties the field, the checkbox should get unchecked.
This should happen any time the user modifies the text field (he is not allowed to change the checkbox directly).

What events are relevent if that field is published on a profile? From what I believe this would be events on profile update/edit, after registration. As Ajax is switched on for this field are there additional events to check on?

Only way to do that is to use CB Auto Actions to add jQuery to the profile edit and registration form display triggers with a Code action and Method set to jQuery. Your jQuery should mark the checkbox checked when the text field keyup event is triggered.