3 hours isn't much for learning XPath
In general, worry more about clarity and maintainability than quantity of code.
XPath is tailor made for XML. It's powerful and easy to read ones you know it. It integrates very well with XSLT and reasonably well with other languages such as Java.
I'll give you some ideas rather than solutions. You navigate the document tree in a similar way to how you would navigate a file tree. E.g. /Game/Round/Door. Counting your rounds could be done like this:
Listing the names of all the first doors:
The [1] makes sure it is only the first door. If you wanted all doors of the second Round:
As a Java programmer you may be used to thinking in Procedures. In XPath everything is about thinking functions. As a Java programmer you might be tempted to iterate over all the Doors, printing "First door:" then doing an xpath constructed in Java with an index you maintain in Java. That's just clumsy. Instead you could use the XPath function
concat in the return expression. Much easier to read (and in this case less code). I leave it to you to figure out the details.