Is classical music folk music?

We don't normally use the term to describe it, but in a manner of speaking some Classical music can be considered folk music.

One of the first big divisions in music is between sacred music (intended for the Church) versus secular music (intended for everyday enjoyment for the 'folks'). Not every piece of Classical music was originally written for the Church, so those pieces might be considered secular, or folk, music in a manner of speaking.

True Classical music is that which was written during a specific time in history called the Classical Period. Roughly the early 1700s to the early 1800s. Today the term is used to describe pretty much any large, orchestral piece. Even a brand new composition is often called Classical music. It's not really accurate, but the term has come to have that connotation in common usage. Today most people hear any piece with a lot of violins in it and call it 'classical' music. ;)

Folk music, in its broadest possible terms, is pretty much anything that wasn't intended to be used in church for sacred worship. If we consider that very wide definition then everything from a simple shepherd tune to deth metal might be thought of as a kind of 'folk' music. But that is a very broad and uncommon way to think of it. Today, as you can tell from many of the questions here, it seems like every time somebody writes a song that's a little different from the others we have a new 'genre' of music.

No, but some classical (not to be confused with 'Classical' - upper case C) composers used traditional folk melodies in their music. Hugo Alfvén, for example, made much use of Swedish folk tunes, especially in his first and third Swedish Rhapsodies. Ralph Vaughan Williams often quoted English folk songs, as you can hear in his English Folk Song Suite - http://www.youtube.com/watch?v=D0sC4xbyT5c The folk songs are: 1. Seventeen Come Sunday. 2. My Bonny Boy. 3. Folk Songs from Somerset.

No, but sometimes a classical composer takes a folk tune (or one or more themes from a folk tune) and works his composition round that. It may be as a theme with variations like Mozart KV.265 : "Ah vous dirai-je, Maman" (also known as Twinkle, Twinkle Little Star) which has 12 variations based on a folk tune.

Strictly speaking, classical music belongs to music composed in the classical period approx. 1730 to 1820.