Did he want to write THE prequel to Figaro? Was Il barbiere marketed as such? Was Figaro even performed in Italy at the time?
And what about Paisiello's Barbiere?
I already asked this question once, but I figure since it's music week I'll give it another try.
Hi! I don't know enough about Rossini to tell you whether he admired Mozart's opera (although I'm sure you can find out about this from a Rossini biography). I can tell you that all the operas you mention were based on a set of plays by the French playwright Beaumarchais, all premiered in the last quarter of the 18th century.
Rossini was definitely aware of Paisiello's Barbiere (which BTW also predates the Figaro). Indeed, the very fact that Rossini was writing a new setting of the Barbiere and having it performed even though Paisiello (who was hugely respected and regarded as a master composer - quite possibly on a par with Mozart!) was still alive at that time, was a huge source of controversy. AIUI, they got around this somewhat by choosing a different title for Rossini's work.