Is Earths orbit with sun is perfectly in horizontal plane ie with the centre of sun?

Answer 1

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.