The "Statute of Anne" (original establishment of something like copyright in British law) dates to 1709 and established exclusive rights on works for a period of IIRC 21 years.
Bach died in 1750; Mozart was born in 1756; Beethoven was born in 1770.
Who is to say we wouldn't also include two or more other great composers in that list if there hadn't been a 21 year statute. Sometimes a set of factors just seem to line up perfectly to generate amazing ideas in the right people - it's why people independently come to the same conclusion or invent the same invention at the same moment in time. Copyright law minimises the benefits of these "golden ages". With longer periods of copyright law (in excess of lifetimes/generations) copyright law can simply destroy the potential value of society.
At the time there was no way of recording music so it didn't protect reproduction of the music in a form you could listen to. But as the court case "Bach vs. Longman" established in 1777 that statute did cover sheet music which was how Bach made money.
http://www.newstatesman.com/music/2008/12/public-century-com... gives a better overview of how the problems of music today are the same problems as back then. This includes a deal of piracy and stealing of works, and also mentions the other problems copyright introduces, such as the dilution of quality. Dickens and Haydn could have created greater works if they weren't focused on public patronage for money.
I'm not going to spend a lot of time researching this, but I know Beethoven had a publisher for his sheet music, and I'm guessing that it was protected like anything else.
Not the point. The business model back then was based around patronage, whether by the church or aristocrats. I'll also guess that the people who voted for the pirate party don't want a move in that direction.