Anything with a star that has planets orbiting around it.
System
"Our solar system." The "part of our galaxy" that's in our solar system is the solar system.
No, our solar system has 8 recognized planets: Mercury, Venus, Earth, Mars, Jupiter, Saturn, Uranus, and Neptune. The International Astronomical Union redefined the criteria for what constitutes a planet in 2006, which led to Pluto being reclassified as a dwarf planet.
Our Solar System is called the Solar System, Why?, what do you Aliens call it.
No. There is one star in our solar system, and no other solar systems within it.
The solar system
The "world" constitutes the planet Earth. There are 8 major planets around the Sun in our solar system, and many more orbiting other stars. (see related question)
My solar system (and yours if you are from Earth) is just called "The Solar System".
When the Moon was formed, the Solar System WAS already a solar system.
There are no exoplanets in our solar system. By definition, an exoplanet is a planet that is not in our solar system.
It is a part of the solar system, however, it is not apart of the solar system.
The Milky Way is not in our solar system. Our solar system is in the Milky Way. There are no galaxies in our solar system.