I am very keen to know about JSP's implicit objects implementation. My simple question is that are they Singleton objects?
They are constant field values. See
https://tomcat.apache.org/tomcat-7.0-doc/jspapi/javax/servlet/jsp/PageContext.html and
https://tomcat.apache.org/tomcat-7.0-doc/jspapi/constant-values.html
Also, if you are using Tomcat, then look in its work folder at a translated file. You will see their creation in the _jspService method.