When do tournament games start? What if my opponent doesn't move?
Tournament games will start when the tournament has finished registration and the tournament director starts the tournament. They can set a date and time, or they can manually start it at will.
As soon as the tournament starts and the pairings are generated all player's clocks start immediately. If no move is made before the time control is up then the game will be auto-resigned as a "timeout" or loss on time (unless vacation is activated, the games will be paused). This affects both player's tournament and Daily Chess records.
The next round of a tournament will start once all the current round's games have been finished. You can see what games are left by clicking on 'pairings' in the menu on the tournament home page.