Is the earth flat?

On YouTube, I was browsing videos while relaxing after a long day of work and stumbled upon a few videos explaining that the earth is actually flat.

You read it correctly.  The earth, being a globe, is a hoax...

Am I missing something or are we losing touch with reality?  I've searched a bit more about that "new" movement and found their website: http://www.theflatearthsociety.org

Their idea is that the earth is a flat static disc having the North Pole at its center and the South Pole on the outer edge.  In their videos, on YouTube, they elaborate "facts" to prove that the earth is flat, often ignoring simple logic and dismissing hard evidences already proven by science.

I have a few questions for those people:

Since we can all see, each morning, the sun rise to the east and set to the west, how does the sun revolves around a disc so that all inhabitants can see it rise from the same side?

How can they explain the shadow of the earth, on the moon during an lunar eclipse?  It is round so the sun would have to be behind the flat earth at a perpendicular angle to cast such a shadow.

If the earth is a static disc, how can they explain winds, streams in the ocean and the different climates?

How do they explain the disappearance of a sailing boat at the horizon?

How is it possible to have night and day around the world at the same time?  Is the sun a really big spotlight?

My favourite "proof" was that aircraft travel time does take the same time going east to west and back.  If the earth was a spinning globe, the aircraft would have to fight against the rotation speed.  Aircrafts are not fighting the rotation but the density of the atmosphere...  Running against a strong wind is already hard enough, be it from the east or the west.  Consider now reaching 250km/h...  

I can admit that some people may fancy strange things but promoting such non sense is just plain crazy.  They theorized that governments are actually setting up a big hoax to make people believe that the earth is round...

What would be the purpose of spending billions of dollars to prove that the earth is not flat?  So NASA is lying by producing fame videos showing that the earth is a globe?  Scientists and astronomers are actually lying to cover their jobs?  I'm outraged!

Have you seen the movie Idiocracy?  You should, it's got electrolytes.