Because the earth is rotating it will continue to do so unless a force is applied to either speed it up, or slow it down. So the answer to the first question is "no force". But the earth is not alone in space. Gravitational attraction from other bodies, particularly the moon, is slowing the rate of rotation. If the sun was no more, then Earth would be drawn to a new centre of gravity. The gravity of Earth and the rest of the solar system would be affected and with there being no constant energy supply from the sun Earth would start drifting into space.