Those are great questions. I'll try rough answers and then go back and fix them up if I find better information.
Your basic description is essentially right. There's a bit of a complication, however, The net force points in the direction to lower the total energy of the vacuum around the pieces of metal. The changes in energy have two terms. The first is that as the plates get closer together, more and more low-frequency vacuum modes are lost for the space between them. That lowers the energy. However, the space between them, with lowered energy density, is replaced with space outside them, with normal energy density. That raises the energy. It turns out that the balance between these opposite terms depends on the dielectric properties of the surfaces and of the space between them. With some surfaces immersed in fluids, the force can end up being repulsive.
The second question is also hard. I don't know whether you have access to a decent vacuum pump. The sorts of very cheap vacuum pumps easily available for home use are driven by water flow, and don't reach vacuums less than the vapor pressure of liquid water. Since the force becomes very small unless the pieces of metal are very close to touching, this is not an easy experiment to perform at home.
As often happens, there's a good Wikipedia article available: http://en.wikipedia.org/wiki/Casimir_effect
(published on 06/29/2009)