How is the galaxy solar system and universe related?

Answer 1

Due to the interactions of two effects, gravity and angular momentum, lighter bodies orbit around heavier ones. In the case of a solar system, planets (and other stuff) orbit around a star; in the case of galaxies, it's the stars that orbit around a central core, or nucleus.

The Earth orbits the Sun in a year; the Sun orbit the galactic core in about 260 million years.

Galaxies do not appear to orbit anything else, because the Universe doesn't seem to have enough "stuff" to provide that "heavier body." Although there is something called the Great Attractor which seems to affect the trajectories of the galaxies, on the whole, they're just spreading out as the UNiverse expands.