Can't see the linked picture. Says access is forbidden.
The whole point of building a Dyson Sphere is to collect all the radiant energy of the sun contained at its center. I guess the Dyson Sphere can be as big as an entire solar system, enclosing the sun and all its planets, or the Dyson Sphere can just enclose the sun and a single planet.
And no, Dyson Spheres don't have anything to do with singularities. If my memory of high school physics is still intact, singularities have to do with black holes, not something you want to live right next to...
Well, as far as our current understanding of physics stands, you can't travel faster than the speed of light. And if you do somehow manage to approach the speed of time, the time dilation effect of relativity would mean that those whom the space travelers have left behind will be LONG dead before the space travelers will have reached their destination. So the more practical thing to do would be to build huge generational interstellar ships, that is, those ships would literally contain mini-civilizations. Or you can build smaller ships and put all the crew into stasis...
Anyways, our solar system is moving, the Milky Way galaxy is moving, in fact everything around us is moving further and further apart, at incredible speeds. It's really not such a stretch to think that we are probably residing in/on a form of planetary "spaceship" right now...