The easiest way to figure out door handing is to stand with your back to the hinges, and whichever side of your body the door is on is the handing of your door. (A left hand reverse door is the same as a right hand door, and a right hand reverse is the same as a left hand door. You only have to take note of the bevel.)
Rekeying is the process of changing the tumblers in a lock so that a new key is required to unlock it.
Rekeying should be done if all keys for a lock cannot be accounted for. High security locks are a good option to limit the need of rekeying because they use secured keyways that eliminate unauthorized duplication of keys.