No. For one thing, a plane is, by definition, 2-dimensional. The moon's orbit is tilted about 5 degrees relative to Earth's orbit.
A lunar eclipse
1). They orbit in the same around the sun, and as the sun. 2). Orbits of planets and their larger moons are in just about the same plane. 3). Almost all planets and moons rotate on their axes in the same direction as the planets orbit the sun.
Earths gravity keeps the moon from flying off in the same way the sun keeps earth in balance.
Most moons orbit their planet the same way the planet rotates. One of Neptune's moons is very different. That moon goes in the opposite direction of Neptune's rotation.
There isn't one. They all orbit in roughly the same plane. Pluto orbits in a different plane, but that's not classed as a planet now, of course.
A lunar eclipse
1). They orbit in the same around the sun, and as the sun. 2). Orbits of planets and their larger moons are in just about the same plane. 3). Almost all planets and moons rotate on their axes in the same direction as the planets orbit the sun.
One of the results of the way gravity works is that a small body in an orbit around a large body moves in a plane. So every point in the earth's orbit around the sun is in the same plane. If you want to be perfectly technical ... the center of mass of the earth/moon system orbits the center of mass of the (sun + all the planets + all their moons) system. But the differences are so small that you can legitimately picture it as if the center of the earth orbits the center of the sun. The plane of the earth's orbit is what we call the "Ecliptic Plane". The orbits of the other planets are in close to the same plane but not exactly.
Earths gravity keeps the moon from flying off in the same way the sun keeps earth in balance.
The Earth orbits the Sun. The plane of the Earth's orbit is called the "ecliptic". The Moon has its own orbit around the Earth, and its own orbital plane. If the plane of the Moon's orbit was the same as the plane of the Earth's orbit, then there WOULD be solar eclipses at every new moon, and lunar eclipses at every full moon. But the plane of the Moon's orbit is NOT the same as the plane of the Earth's orbit - and really, why would they be? The Moon's orbital plane is inclined by about 5 degrees from the ecliptic. Therefore, eclipses only happen at full and new moons about every six months, when the Moon happens to be crossing the ecliptic.
I know Saturn has two moons in more or less the same orbit. I'm not sure about three moons though.
yes
The same way it affects most of earth. The seasons are caused by the tilt of the earth's axis relative to the plane of its orbit.
Most moons orbit their planet the same way the planet rotates. One of Neptune's moons is very different. That moon goes in the opposite direction of Neptune's rotation.
Most but not all larger MOONS (bodies that orbit planets, moons, or asteroids) accreted in the same way that PLANETS did, assuming a variable density and a nearly spherical shape. Very large moons such as Titan have many of the characteristics of planets: vulcanism, atmospheres, and weather. Generally speaking, moons orbit planets in the same way that planets orbit stars.
The moon's orbital plane is inclined about 5 degrees to the ecliptic. If the earth's and moon's orbital planes coincided, there would be a solar eclipse at every New Moon, and a lunar eclipse at every Full Moon. Pretty spectacular, but we would think that's just the way things work, and nobody would give it a second thought, like the miracle of the daily rising and setting of the sun.
The direction of the Earth's spin and the direction of the Moon's orbit is the same - counterclockwise