The earth rotates itself and rotates around the sun.
a full rotation around the sun is exactly a year.
a full rotation of the earth itself is a day.
Yes.
the gravity moves the Earth in a circle
yes
The Earth moves around the sun due to the warping of space time that we perceive as gravity.
Both would probably move away from each other, because the earth moves too.
they are pulled by the Earths gravity
well space is like a vacuum you cant escape it and sound wave do not travel in space but space isn't literally a vacuum so they move by rockets and the gravity of earth
Earth has gravity so less fuel is needed to move a rocket in space(assume that you mean escape from earth's gravitational field by"from earth")
No I don't think so.
the gravitational pull of the earth moves the moon
It moves in Time, the fourth dimension.
Yes, you are not in space so you are still in Earth's gravitational force.