How is it possible that only the bottom half of the moon was showing?
It depends on the season and even more on latitude.

At any given time, the same side of the Moon faces the Sun.  Where you stand on Earth doesn't change which part of the Moon is lit, but if you think about the orientation of people on the earth, people in the Northern and Southern Hemisphere are "upside down" to each other and people on the equator are perpendicular.   The Moon doesn't change but the point of view of people on Earth relative to the Earth's surface makes a full 360 degrees of rotation based on latitude, so the same moon at the same time can appear as a left crescent, a right cresent, a boat and a yamaka depending on the person's latitude at the time of viewing.

Also explained here.

And this should probably be astronomy.