Take a look at Lectures 7 and 8 here:

http://emlab.utep.edu/ee5390em21.htm

The website has electronic notes as well as recorded videos, but some of the electronic notes have been revised a bit since the videos were recorded.  I think you will find this information rather intuitive with a lot of pictures.

Yes, the BZ is simply the Wigner-Seitz unit cell in reciprocal space.  So, just like the WS unit cell, the BZ is uniquely described by just three lattice vectors (not wave vectors), called the reciprocal lattice vectors.  In a sense there are no BZ boundaries just like there are no unit cell boundaries.  You can simply translate the unit cell boundaries just a little bit and you will still have a perfectly valid unit cell.  There are locations that make the unit cell boundaries more intuitive, but that is an artificial thing.  Think of the BZ as a map of how similar the physical lattice is in each direction.  The more spherical the BZ, the more similar the lattice looks to waves in all directions.  This is called the degree of symmetry.  In this framework, it may make more sense why the BZ has no boundaries.

Thanks!

You can define the Brillouin zone(BZ) as the Fourier transform of the lattice of your material, that is true, but it is hard to understand why is useful only by its definition. In order to understand its use, you need to first understand the Bloch theorem, this theorem state that the spectrum of a infinite periodic system can be described in terms of plane-wave like eigenstates. These eigenstates are labeled by using a quantum number k, which are the points in the Brillouin zone. In this answer that I gave in Quora I explain how it work for graphene https://www.quora.com/How-is-it-that-electrons-act-like-massless-particles-in-graphene