The messages written by a Player Moderator can be seen even by players who have turned their public chat off.
Private messages sent by a Player Moderator are also visible when private chat is turned off though Player Moderators are unable to send subsequent messages or see that the player is online via his/her friends' menu.
Although you do not have to play a certain amount of time, most moderators have played one year or more before being asked to join the team.
It is mentioned that being on the forums helps being noticed.
This is to settle in new moderators into their role as part of a training period.