Every electron has a magnetic moment, which is related to its spin. I will list a Wikipedia reference at the end but please bear in mind, if you don't know already, that spin is this case is both fixed in magnitude and also has nothing to do with the physical spin of a very small soccer ball. It's more a shorthand word for spin angular momentum
The magnetic moment of a magnet is a quantity that determines the torque it will experience in an external magnetic field. The magnetic field produced by the magnet is proportional to its magnetic moment. More precisely, the term magnetic moment normally refers to a system's magnetic dipole moment, which produces the first term in the multipole expansion of a general magnetic field.
Why an electron has this magnetism associated with it, and how exactly it is physically related to spin is unknown, it just has....
So what I understand know, is that every electron has a magnetic moment. If you have a material of a certain size and you add up all the magnetic moment resulting in a net magnetic moment, then the material is magnetic. 3) Is that right?
The size of the material is not important, what is important is that some materials, such as iron, can have their electrons lined up in clumps (domains), all pointing roughly the same way, so you have a net overall magnetic field. With most materials, such as a piece of paper, this does not happen, and the net magnetic field is zero, that is the electrons are pointed randomly.
Does the magnetic moment has something to do with the magnetic fields created by the moving electrons ( Lorent'z law) ? Before reading about magnetic moment, I thought that a material was magnetic due to the fields created by moving electrons. So to sum up this last part, I want to know if there is an relation between magnetic moment of an electron and the magnetic fields created by the moving electrons. Are they the same thing, or ?
All electrons have intrinsic magnetic moments, whether they are moving along a wire or not so no, they are not the same thing/ effect, to sum your questions above. We can use an external magnetic field, created by moving electrons, to influence the magnetic moment of electrons.
Magnetic Moments is worth reading. As is Producing magnetic fields and this more straightforward article: Hyperphysics magnetic fields relating to your last question.