Is it possible for a clock to show less than 30 seconds for a player in a game with a 30-second increment? Is it possible for a clock to show less than 30 seconds for a player in a game with a 30-second increment when it is his opponent's turn? 

My answer:

Even if one player has only 1 second on his clock and then makes his move, he would end up with 31 seconds on his clock and it is his opponent's turn. So, it seems to me that a clock under such time controls can never show less than 30 seconds for a player when it is his opponent's turn.

Am I wrong?
You are correct - it is impossible. It can only show less than 30 seconds while it's counting down on his/her turn.

Obviously, with delay instead of increment, this would be possible.