Do asteroids orbit the sun?
Yes. There is an asteroid belt between mars and Jupiter.
Affirmative. Most asteroids do orbit a sun. It doesn't have to be our Sun, but any star in the universe. Although there are many other entities out there, the asteroids mostly orbit the suns. If you took an asteroid and put it to orbit a centre of the galaxy, it would rather fast be attracted by some solar system and begin orbiting it.