If the earth is round why can i see the moon during the day

This is what's called a lunar eclipse. Not only does the moon appear to change shape by way of an optical illusion, it also appears to move across the sky. Just as the sun appears to “rise” and “set,” the moon's daily trips across the sky are mostly created by the rotation of the Earth.

Yes, everyone sees the same phases of the Moon. People north and south of the equator do see the Moon's current phase from different angles, though. If you traveled to the other hemisphere, the Moon would be in the same phase as it is at home, but it would appear upside down compared to what you're used to!

The only times you won't be able to see it during the day are near a new Moon, when it is positioned too close to the Sun in the sky to be seen, and near a full Moon, when it rises at sunset and sets at sunrise, so is only visible during the hours of darkness.