When I start guiding, the star initially stays put, but then starts moving rapidly back and forth until it leaves the guide box. What is wrong?

The autoguider is not calibrated properly. Go to the Guide tab Settings and set the X and Y backlash to zero. Set the X and Y Cal. Times to 20 seconds, or the highest you can use without the star going off the chip during calibration. If selectable, set your mount to 0.5X guide rate. Find a bright star and run the calibration procedure. Now try guiding on that star. If it still oscillates, try reducing the Agressiveness setting.

Remember, if you change Declination, you must either use the declination compensation feature or recalibrate. If you are not using the declination compensation feature, just leave the setting at 0.