A: No. You can compile and test your own robot using the off-line package. Then you upload the class file to the site. That file is automatically recognized by the applet that simulates tournaments.

A: Send a file with the same name. The old file is overwritten and the new robot inherits the results of its predecessor.
If you choose a new name you send a robot that can fight against the old one.

A: Case 1 In the program that controls your robot you catch an exception, so in the class file a java.lang.Exception class appears. In such a case a rule was broken: "You can't use the classes of the Java API in the code of your robot"
Case 2 In the program that controls your robot you use the java.lang.Math class to get the PI constant, so a rule was broken: "You can't use the classes of the Java API in the code of your robot". Define yourself the PI constant in the code of your robot.

A: Case 1 The robots can't use inner classes, sorry. All the algorithms must be in a single class. Your robot uses two classes MyRobot.class and MyRobot$1.class. You can upload only a single class, so MyRobot$1 was missing in the on-line version and an exception was thrown.

A: I use an unusual convention to speed up simulations on slow machines, because calculations are simpler. This is not a problem: the robots can't see the applet and you can watch the arena from the underground ;-)

A: If you use the JDK and the appletviewer, it's really simple. For example you can use this code to print a variable ('a' is an integer variable or whatever else):

System.out.println("the value of 'a' is: "+a);

A: There is a security issue with finalize(). That method must be called from the main thread when a robot dies, so the main thread gives control to the code of the robot. Someone could put an infinite loop in finalize() to stop execution and to avoid the negative result.
To identify the robots check the id() method when the main() method starts. It gives a unique identifier according to the order of creation of the robots.