Is the sun a star in the milky way galaxy?
Yes, indeed it is- it is towards the outer fringes of the West spiral arm of the Milky Way.
Earth's Sun is a star in the Milky Way galaxy, believed to be a spiral or barred spiral type of galaxy. The name "Milky Way" comes from the dense nighttime band of stars when looking up into the plane of the galactic disk. Earth is located in the Milky Way Galaxy. The Earth is located on the Orion arm of the galaxy. The Milky Way Galaxy is made out of roughly 200 billion stars.
...only as a metaphor. The Earth is a planet that is in the Milky Way galaxy. The Earth is not a galaxy. No, the Earth is a planet which orbits the Sun (which is a star) along with several other plants, this is called the solar system. Our Sun and its planets along with millions of other stars form a galaxy called The Milky Way.