I want to add a field in the defect screen. How do I make it required? Also, How do I make subcategories such as Jazz's own defect management where you have something like a Report, then subcategories under it?

To make some field required on work item:

Open Project area, then go to Project Configuration. Select Team Configuration and Operation Behavior.
On the right site you 'll see window with operations and roles. There is a last operation work items, and you need to click in empty cell of role for which you want to make required field or you can do it for everyone (all roles).
After clicking, you 'll see preconditions and follow up actions, where you must add required properties.
Then, you can select transition state where your attribute will be required. Double click on state and select required properties. That should work.

Regards,