The COR rating designates the hardness of the ball. The higher the rating the harder the ball and therefore, the higher performance it will have. ASA regulates the COR rating as a safety measure.
As for your other questions, the tie always goes to the runner, the mechanic is the same as "safe" and the only jumping is done by the coaches when you fail to make this call ("Tie goes to the runner" - Jim Booth's baseball myth #16 - also applies to softball).
You probably missed the "table" because it is so small - it is just a clipboard the scorers use, and the possession arrow is actually called a "half-inning"
[Edited by Dakota on Mar 5th, 2001 at 05:02 PM]