I suggest starting with the simpler BorderDetect example that comes with the Zumo Shield Arduino Library. This example has some of the behavior you described already (e.g. roaming around the ring and detecting the edge of the ring). Then after you get it working, you could go back and add the collision detection methods from the SumoCollisionDetect example if you still want to.
You can read the Sharp analog distance sensors using the Arduino's analogRead() command. How many Sharp analog distance sensors are you using? If you are using one, you could use that to just speed up the robot when it senses the opponent. If you are using two, you could cross reference the sensors with the motors. This way if the right sensor sees the opponent, your left motor would speed up, turning towards it. Similarly, your left sensor could speed up your right motor. Then, if both sensors see the robot, both motors would speed up.
If you try editing the example or writing your own code and run into problems, you can post your code here, and I'd be happy to take a look.