Question: Is there a Java Web Framework, with mvc, thrid-party integration APIs, libraries and tools? Something like Zend Framework for PHP?

Answer: 
Using Zend for a while, I found the transition to Spring fairly easy.
Spring does come with more bells and whistles (Dependancy injection, AOP etc)
There are a lot of Java web Frameworks, here you have a list with lots of them: <http://java-source.net/open-source/web-frameworks>

The most "famous" would be Struts, JSF or Spring mvc framework (not in that particular order).