no it isn't the earth is a little flattened around the poles
A circle is a two dimensional object. I think you mean are they spheres. In general, They are, but not perfect spheres. The equators bulge out slightly
Yes
the earth circles the sun while the moon circles the earth
The moon circles around the earth; the earth circles around the sun.
The moon orbits the Earth, which orbits the sun.
the earth is a bit flattened but the moon has a brilliant circle
The moon circles the earth...
the earth is a bit flattened but the moon has a brilliant circle
not quite. The moon circles the Earth, which circles the sun. So the moon's orbit around the sun isn't a smooth track, but consist of a wave like pattern.
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).
Basically because the moon revolves around the earth so therefore it circles the sun to. It doesn't orbit it but it does go around it.
The moon circles the earth once every 28 days approximately. It keeps the same face towards the earth at all times and so as it circles the earth this means that, relative to the sun, it rotates once on its axis in this time. Therefore the moon shows its rear side towards the sun when it is a new moon (and the face of the moon facing earth is dark), and its earth-facing sun towards the sun when it's full moon (and the moon is bright). This new moon and full moon cycle lasts once every fourteen days. Therefore the moon's night is 14 earth days long, and its day is also 14 earth days long.
The Phases of the Moon are caused by the amount of lighted Moon surface that is visible from Earth. That changes in standard cycles of 29.5 days as the Moon circles the Earth and the Earth circles the Sun. Half of the Moon is always lit by the Sun, the same as all the planets and satellites. At different times of the month, different amounts of that lighted surface are visible from Earth. If the Moon is between the Sun and Earth, we see only the dark side. If the Moon has circled to the other side of the Earth, away from the sun, we see the lit side. For instance, at the time of the Crescent Moon, the whole Moon is there, but we are seeing (or not seeing) mostly the unlit side of the Moon. At that time, because of the positions of the Earth, Sun and Moon, only the edge of the lit part is visible from Earth.
The moon does not circle the sun directly, it circles the earth. so it would be approximately the same as how long the earth takes, about 365 days.