Those dust grains served as condensation centers for the formation of larger molecules and even larger grains. The solar wind, which envelopes all the planets, is still dominated by Hydrogen and Helium nuclei and their ionized electrons.
Some asteroids are even binary pairs, orbiting around each other.
These days, literally dozens of asteroids are discovered and named each month, most of them smaller than 1km across. All members of the Asteroid Belt orbit the sun in the same CCW sense as the planets. The answer is, of course, gravitational. Each time an asteroid in the Belt came close to Jupiter, that object's orbit was disrupted by the massive planet's gravitational pull. The only asteroids remaining in the belt are those whose orbits do NOT take them close enough to Jupiter to be disrupted.