quantum field theory - Virtual Particles real? Virtual particles create a universe?

I am reading the book of Lawrence Krauss "A universe out of nothing", where he explained that the vacuum is not empty. It is a boiling brew of virtual particles that come out of their existence. And they can create a universe, even space.

But virtual particles are inner lines in a feynman-diagram. They converge in a vertex and so on. They are off-Shell.

I am a layman and I cannot grasp clearly about this stuff.

My question are:

1. 
   

   Is the vacuum empty or is it not?

   
   


2. 
   
   

   Are there particles in the vacuum and can they create a universe?

   
   


3. 
   

   But when virtual particles are just a mathemacical "trick" to calculate something, what does Lawrence Krauss mean?

   
   


4. 
   

   What is the matter about the vacuum?