Yes. You do not have to write down the move when under 5 minutes unless there is going to be a second time control.
Interesting question. We best must consult an arbiter.
USCF rules state that once youre below 5 minutes you dont have to write your moves down. If youre playing with a 30 second increment then you are required to write your moves down.
^You're* Had to.
All I really know is that if you have under five minutes, you stop recording.
In a logical sense, you would have to keep recording when you have 30 sec increment.