While your goal of learning modern JSP is good, I'm not sure that you are going to get many offers of people giving away entire web apps for free. Perhaps someone knows of a good open source project that would be suitable.
There is a good book about web programming by Murach. The book teaches the programmer by building a complete web application for a music store that is selling music online. The data is in mysql, tomcat server is used , etc. If you register with Murach after you purchase the book they send a zip file with all the source code including the scripts to create and load the mysql database. The application includes a shopping cat, catalog search, and so on. The exercises teach you by having you alter the code that you download.
Murach's JavaServlets and JSP. Andrea Steelman, Joel Murach, Andrea Steelman, Joel Murach. Mike Murach & Associates. second edition. January 2008. 758 pages .
It is on javaranch in the book reviews, Reviewed by David O'Meara, April 2008, (10 of 10) .
Here is the description from Amazon.com
This new edition of Murach's Java Servlets and JSP makes it easier than ever for Java developers to master web programming. It starts by showing how to install and use Tomcat as a web server and NetBeans as an IDE. Then, it teaches how and when to use JavaServer Pages and Java servlets to build well-structured web applications that implement the MVC pattern. Next, it shows how to use sessions, cookies, JavaBeans, Expression Language (EL), the JSP Standard Tag Library (JSTL), and custom tags. Then, it shows how to use JDBC and connection pooling to work with a MySQL database. Finally, it shows how to use JavaMail, SSL/TLS, authentication, listeners, and filters. These are the skills that you need to build professional Java web applications.