The same star would be brighter if it were closer to Earth. However, there are other attributes that affect the stars brightness, such as size and temperature. So a further star can actually be brighter than a closer one if it were bigger or hotter.
The short and simple answer to that question is yes. In a way that is what scientists use to measure distance. Though, to understand a little bit more about why and how of star measurements go to the link below.
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