I don't know either exactly what makes a language "agile", but Groovy let's you put something together quickly.
Depending on your style, quite a lot. You can leave out a lot of Java's boilerplate code, there are no checked exceptions etc.
Yes, without problems.
Another way that you write less code is that you needn't catch or explicitly throw any exceptions. Obviously, it's up to you to make sure that your application recovers gracefully from errors, but this is really nice when you are writing a script that does some file I/O.
One of the most important resources to understand how your code can be shorter is the Groovy JDKwhich lists the methods that Groovy adds to your familiar Java objects.
3.Yes, this is the biggest advantage of Groovy over Python or Ruby.
4.I've enjoyed it a lot, particularly in connection with Grails. But if I find myself working on a Java team, I expect to use Groovy for scripts, and for test code, when possible. The biggest disadvantage is the tool support, Eclipse and NetBeans are not ready for prime-time with Groovy. IntelliJ makes it tolerable. Ultimately, Groovy successfully removed most of the boring and awkward parts of Java.