Do all the stars that we can see with the naked eye belong to the Milky Way galaxy?

Answer

All the stars that you can see with the naked eye belong to our galaxy, and even to the immediate vicinity of the sun.
However, it is not possible to set a maximum distance on it. Why not ?
The apparent brightness with which we see a star in the sky depends on two things:

– the actual brightness of the star, the so-called absolute brightness, and
– the distance at which she stands.

For example, it is quite possible that a faint star in the sky is in reality a whopper, for example a blue or red giant, which we can hardly see due to its great distance. The reverse is also possible: a star that is actually very faint, we see brighter because it happens to be at a shorter distance.
A star like the Sun is visible to the naked eye from a distance of about 30 light years. Supergiants are visible from a distance of several thousand light-years or even ten thousand light-years. But compare that to the size of our galaxy: 100,000 light years