Is it possible to move a planet out of its orbit? At least a lighter planet? As observed by many researches our sun will be exhausted in the distant future. So does anyone think that driving our planet (or any planet) closer to the sun for more light and heat is a solution for life to survive on earth? Or would moving it out of the sun's gravitational field and taking it to some other solar system with a healthy star be better, possibly with some kind of thrusting mechanism that we may invent in future?

I am aware of the sun's gravity and the mass of the earth.
Yes. Even with todays technology we can get started.
In this article by Korycansky et al 2001 it is suggested to use rockets to move an asteroid (like a larger version of the NASA ARM Asteroid Redirect Mission) to a cycling orbit between Earth and Jupiter. The asteroid would pass near infront of the Earth in order to give the Earth a slight gravity assist which moves it outwards. The asteroid then passes near behind Jupiter to itself get a gravity assist. This transfers energy from Jupiter's to Earth's orbit. I've also heard of a proposal to use Venus instead.