How and when can I delete a started game? Is the deleted game counted for my statistics or BKR?

You can delete a started game until both players made two moves only. It means that after the player who has not started the game (black player) performs his/her second move, nobody can delete this game anymore. The main purpose of this feature is to allow players to get rid of a game where the opponent did not start to play at all without waiting for a timeout.
If your game can be deleted, i.e. it fulfills the previous conditions, a link "Delete game" will be added to the bottom of the game page, just nearby "Offer draw | Resign" links.
A deleted game is not counted for anything. Statistics of both players (number of won, drawn and lost games) will stay unchanged and the game will not be calculated for the players' BKR.