Tutor profile: Javier B.

Is it true that all really great classical music comes form J.S. Bach?

Of course. Let's look at it this way. During the 19th century, the biggest influence on composers was probably Beethoven. Now, Ludwig's own major influence can be traced back to the classical period naturally, in the likes of Haydn, and Mozart. So who is Mozart's and Haydn's biggest influence? A nowadays little known composer by the name of Johann Christian Bach, who was a son of Johann Sebastian Bach, so there you go!

Is it impossible to reconcile the notation usually used for derivatives, $$\frac{dy}{dx}$$, with the notion of this being an actual fraction, of "dy over dx"?

It is not impossible at all. You just have to think of the dx's as k-forms.

What is the connection between one-parameter groups of diffeomorphisms and differential equations?

Every differential equations defines a one parameter group. The orbits of which, are the solutions of the equations.