The gas and dust that collapsed to form the solar system aquired a rotation in a particular direction during collapse. The resulting orbit of all the planets and most other objects in the solar system is a result of this initial rotation.
The Earth and all other objects are attracted to the Sun via gravity.
See here: http://en.wikipedia.org/wiki/Dynamo_theory
I can't say anything on rotation, but when a black hole or neutron star "sucks in" matter, it isn't like a vacuum cleaner. The material FALLS toward it just like a spaceship falls to Earth during reentry. The diameter of most black holes and all neutron stars is very small, only about 10-20 kilometers, and the material spirals down into it. During this process it collides with other material and gets compressed, generating EM radiation sent out as light, x-rays, etc.
As I explained above they do not suck anything up. They simply have extremely high gravity. When an object such as a star gets close to a black hole the side nearest to the black hole is attracted to it more than the other side is. If this difference in attractive force is strong enough it can rip material from the star and even rip the entire star apart.