where do the cookies get stored in the request object

Cookies are stored in the headers. In the response header it is stored at Set-Cookie and in the request object it is stored under Cookie header

Is the exception implicit object available in all the JSP pages?

No, it is avaliable only in the error pages. that is in the pages where this directive is present

<%@ page isErrorPage="true" import="java.io.*" %>

how do you navigate to error pages in JSP

In the page where exception might occur, add a page directive as below

<%@ page errorPage="ExceptionHandler.jsp" %>

Here ExceptionHandler.jsp is the actual error JSP to which exception implicit object is made available when exception occurs. Inside this page we need to add a page directive as shown below

<%@ page isErrorPage="true" import="java.io.*" %>