Success tomorrow means partial freedom from Mother. Failure means they will lag behind the others in their progress. To lag behind the others is to lag behind all the dragonlings hatched in their cycle.
Fourth was the only one not concerned. It is because he has already succeeded in the second training. He has just been waiting for this moment to show off.
Unlike the others, who couldn't sleep because of anxiety, he couldn't sleep because he was too excited. The four of them stayed by the opening of the cave, looking out into the darkness and waiting for the sun to rise.
The cycle of light and day is not fixed in the dragon continent. This is because the position of the plane is not fixed. It moves about freely in the realm. Daylight comes when they move into the path of either of the suns. The addition of the third star has only made things more random. But it has increased the amount of daylight that they experience. So they didn't have to wait long for the sun to rise.