We do not have a good grasp of other existing planetary systems to be able to answer the second part of your question.
Is our solar system moving.
The sun rotates as it orbits the center of the milky way.
But since the nearest star is many light years away i would not concern myself with that too much.
The sun and the solar system appear to be moving at 200.
Is not the only motion we have in space.
If we ignore the earth s rotation and revolution around the sun we find that our solar system is moving relative to the cmb at 368 2 km s.
When you throw in the motion of the local group you.
Another piece of evidence for the sun centered solar system comes.
Our solar system is moving along with the galaxy of course.
The solar system is the gravitationally bound system of the sun and the objects that orbit it either directly or indirectly.
Yes but in a relative sort of way.
Of the objects that orbit the sun directly the largest are the eight planets with the remainder being smaller objects the dwarf planets and small solar system bodies of the objects that orbit the sun indirectly the moons two are larger than the smallest planet.
In order to keep us in our stable orbit where we are we need to move at right around 30.
Our orbital speed.
But even at this speed it takes us about 230 million years to make one complete orbit around the milky way.
So if you combine the motion of the planets around the sun with the motion of the whole solar system around the center of the galaxy you do get a kind of.
Our solar system is moving with an average velocity of 450 000 miles per hour 720 000 kilometers per hour.
It is also moving though rather slowing within the galaxy.