Is ISS orbiting with or against the rotation of Earth? Is it important in any aspect for the space station?
The ISS orbit is prograde - in the direction of the Earth rotation. Prograde orbits are orbits with inclination less than 90 degrees. ISS inclination is 51.6 degrees.
These orbits are slightly easier to reach, because they don't require as much fuel, as you get additional "kick" from the Earth during launch. Retrograde (opposite direction) orbits are rare, because they require more fuel to reach. It would be inefficient to build the ISS in retrograde orbit, because all the craft would have to spend additional fuel to get there. The ISS orbit was chosen to make it accessible from the key launch sites in United States (Florida) and Kazakhstan (Baikonur).