If you mean to ask what is the effect of gravity on a rotating body then I suggest you try two experiments:
1) Spin a small steel ball up to 15,000 to 20,000 rpm in vacuum and drop it.
2) Drop two magents from a height. One rotating at high speeds and the other not rotating.
You may or may not get interesting results.
Not sure what you mean exactly; any rotating object has an axis of rotation.Without gravity, there would basically be no Earth, though.
Your question isn't exactly stated correctly, but the result that I believe you are looking for is that, the object will be in Orbit around the Earth. This happens when the Centrifugal Force (outward from the rotation) balances out against the Pull of Gravity (Inward). For a body rotating about the Earth, the inward Force would be the Force of Gravity, which would account for the Centripetal Force. Gravity is 'taking the place of' the piece of string that holds an object in place when it is swung around in a circle.
The sun's rotation does not cause gravity. Gravity is a fundamental force of attraction between objects with mass, and it is always present regardless of whether an object is rotating or stationary. Rotation affects other aspects of a celestial body's behavior, such as its shape and magnetic field, but not the force of gravity itself.
A planet is a large rotating body that is held in orbit by a star's gravity in a solar system.
The amount of gravity acting on an object is its weight. Weight is the force exerted on an object due to gravity, and it is directly proportional to the object's mass.
Any object with mass affects gravity
Any object that rotates has a tendency to continue rotating.
No, but the centre of gravity need not be inside the object. Not unless Gravity is not a variable. But it is not possible for an object to not have a center of mass.
Acceleration of rotating objects
The weight of an object is the force of gravity.
It doesn't work like that. You don't need power to keep an object rotating. Any object that is rotating will continue rotating, unless it is slowed down, by friction for example.
weight is defined as the product of mass and gravity constant. as the value of gravity changes weight is also changed