After installing IAR, is it mandatory to have a registration key or any other specific license for the software to be used ?

You require a valid license to work with IAR. After installation IAR will ask for the License details.

Please note this is not ADI tool. 

• There is document related to License information of IAR : updates.iar.com/.../LicensingGuide_LMS2.ENU.pdf
  This document consists information on License types, Installation of License, License management etc.
• The FAQ's related License are present in the link : www.iar.com/.../