Let's compare definitions here astronomically. A solar system is a set of planetary bodies orbiting a star. A galaxy is a massive collection of stars. The Milky Way is the name for the galaxy in which our solar system resides.
So the answer to your question is not only yes, but repeatedly yes. Hundreds, thousands, even tens of thousands of solar systems exist within our galaxy, and within every galaxy in the universe.
The Hubble Space Telescope has already identified more than 400 planets outside of our solar system within the Milky Way Galaxy, including some which appear to have atmospheres and water or ice.
Yes! there are many I mean even thousands.
Ex - Kepler 22 system where there may be life. 95%
Hello! Yeah the Kepler22 system.