Would the music of someone like Mozart have been accessible to everyday folk back in his time, as it is now? Would a commoner have been familiar with his music?
Obviously Mozart is dead. However, the demand for his music is still alive. Therefore, his music is conducted by people other than himself. Would someone other than Mozart have conducted his music while he was still alive? If not, how could one person meet all of the demand for their music across Europe? They didn't have radios to broadcast it to millions of people.
How would the status of classical musicians in their day compare to that of modern musicians? Were they comparable to modern celebrities, like famous rockstars, or is this a false equivalency?
Would the music of someone like Mozart have been accessible to everyday folk back in his time, as it is now? Would a commoner have been familiar with his music?
Urban middle class folks, yes. These were definitely part of the audience Mozart catered to. Rural and lower classes? That's harder to tell; they probably wouldn't have been familiar with Mozart's music specifically, and what we call nowadays "folk" music features a rather different and perhaps more archaic style.
Obviously Mozart is dead. However, the demand for his music is still alive. Therefore, his music is conducted by people other than himself. Would someone other than Mozart have conducted his music while he was still alive?
In the 18th century, the way it worked generally is that if you were a wealthy patron, you would hire a kapellmeister ('director of music') to compose original music for your orchestra. So it would've been rather natural for Mozart to "conduct" his own music, generally by playing continuo (or what we call "comping" in modern music) from the keyboard. Mass music publishing was just getting started back then, and then only for comparatively "popular" genres like solo and chamber music, not "orchestral" works! Manuscripts could be sent around and music could spread in this way, but this was very much the exception, not the rule.
How would the status of classical musicians in their day compare to that of modern musicians? Were they comparable to modern celebrities, like famous rockstars, or is this a false equivalency?
It partly depends what you mean by "musician" there. Composers like Mozart would've been considered akin to successful craftsmen, though Mozart was also a notable piano performer and this would boost his status to some extent. The highest degree of notability and fame was enjoyed by star opera performers, and we might perhaps loosely compare this status to modern "rockstars". None of these roles though would confer a truly "higher status" in a courtly sense; even the most successful performers would've been regarded as mere commoners.