Is it possible to draw a conclusion about its distance from the Earth, size, luminosity and other characteristics based

Is it possible to draw a conclusion about its distance from the Earth, size, luminosity and other characteristics based on the appearance of a star?

Such a conclusion cannot be drawn. Stars are at different distances from the Earth, which the eye cannot discern. Many stars appear bright only because of their relative proximity to the solar system, but in reality they are much fainter than barely visible stars located at unimaginably large distances.
To find out the actual luminosity of stars, the magnitude is calculated under the condition of the same distance.
For many stars, the difference between apparent and absolute magnitude is very large. For example, the apparent stellar magnitude of the Sun is -26.7m, and its absolute magnitude is + 4.8m. This means that from a standard distance (32.6 light years), the Sun would look like a barely visible star.