What shape are the earth and moon?
Ignoring stuff like mountains, almost perfect spheres. Because of spin, the polar diameter is slightly less than the equatorial diameter (oblateness).
The shape of the moon changes to us on Earth because of the position that the Sun, Moon, and Earth are in at the time. If the Sun, Moon, and Earth are at a 180o angle withe the moon and sun on the out side then we will have a new moon because the earth will be blocking all the light away from the moon.
No, it has nothing to do with the shape of the Earth. Phases of the Moon are caused by the relative positions of the Sun, the Earth and the Moon. When seen through a telescope, Venus presents similar phases. However, the circular shape of Earth's shadow that is projected on the Moon' surface during a lunar eclipse is evidence that the Earth is round.
As the moon circles the Earth, the shape of the moon appears to change; this is because different amounts of the illuminated part of the moon are facing us. The shape varies from a full moon (when the Earth is between the sun and the moon) to a new moon (when the moon is between the sun and the Earth).
The moon does not change shape as it orbits Earth. The reason it looks as if it is is because of the light reaching the moon in reference to its position to the sun. The position of the moon around the Earth at different times of the year only allows for light to illuminate certain areas of the moon at certain times, giving it its visible "shape".