Is a galaxy an area of sky and all the stars visible in that area?

No, a galaxy is not simply an area of sky with visible stars; it is a massive system that contains billions to trillions of stars, along with gas, dust, and dark matter, all bound together by gravity. Galaxies can span thousands of light-years across and exist in various shapes, such as spiral, elliptical, or irregular. The stars we see in the night sky are only a small fraction of the stars that exist in our own Milky Way galaxy, let alone in other galaxies throughout the universe.