What excellent questions!
Yes, magnetism is a relativistic effect and it is for the most part caused by electron spins, and these are two sides of the same coin.
I recommend the book by my freshman physics teacher, Ed Purcell, for a beautiful introduction to the connection between magnetism and relativity. It turns out that in order for phenomena to follow the same laws in all reference frames, the electrical force has to be accompanied by a velocity-dependent force, which we call magnetism. The same reasoning applies to other forces, in particular the nuclear forces, but since they were discovered after the relativistic argument was understood, nobody made up special names for their velocity-dependent parts.
We have many other answers on ferromagnetism, so why not check those and get back to us if you still have questions on it.
(published on 01/11/2010)