moonless night and lunar phase How to define moonless night? There is no moon at all during some night?  
How to calculate and know whether the moon would appear during one night?

If the lunar phase is full moon, is it possible that the moon will not appear ?
A moonless night is, as you suspect, a night in which the Moon does not appear visible in the sky. This happens once per month, when the Moon is near the Sun. Due to the proximity of the Moon and the Sun in the sky, at that time the Moon is the smallest sliver possible, and therefore not a full moon.

This is because it is actually the Sun that illuminates the Moon, and when the Sun and the Moon are in the same direction in the sky we are seeing the non-illuminated side of the Moon. Note the direction of the sunlight in this image:



Obviously, the direction of the sunlight is the direction of "up" during the day. If you look at the horizon slightly after sunset or slightly before sunrise, you might actually catch a glimpse of the sliver of Moon before it set or rises slightly after or before the Sun.