Electron Spin

Every particle has an intrinsic angular momentum, known as spin. It helps to think of each particle as spinning like a top, but spin is a wholly quantum mechanical concept, it really does not have an analog in classical physics. For instance, if a proton was spinning at the rate required to generate by its spin, its surface would be travelling significantly faster than the speed of light. So, while the spinning top analogy helps, its not really a good description. The truth of the matter is that spin is another degree of freedom.

Nothing. Every quantum mechanical particle has some intrinsic angular momentum that never dissipates. Particle are divided into two classes by their spins: Fermions and Bosons. A particle with an integer plus 1/2 for its spin (+/- 1/2, +/- 3/2, etc.) is called a fermion, e.g. electrons, protons, neutrons, etc. A fermion obeys the Pauli exclusion principle which says that two fermions cannot occupy the same state at the same time, i.e. they cannot have the same quantum numbers. This causes electrons to fill shells. Take helium with its two electrons, for example. Both are allowed to be in the ground state, provided that they have different spins. A particle with an integral spin (0, +/- 1, +/- 2, etc.) is called a boson, e.g. all force carrying particles like the photon, gluon, graviton, etc. Since, bosons do not obey Pauli exclusion, they can all condense into the ground state. (See this for more info on Bose-Einstein condensates, and this for another example.)

Because a particle has a spin, it also has an intrinsic magnetic moment, even neutrons which are electrically neutral. This was how the spin was initially discovered. Simply put, silver atoms (which are a composite particle with a definite spin of 1/2) when shot through a non-uniform magnetic field will split into two groups: one with spin-up, one with spin-down. Also, the electronic spin is the primary cause of magnetism in materials.

Good question. Unfortunately, it requires the weirdest answer: not as such. Now, in both the news posting and above in the comment, I have been talking about spin-up and spin-down, so the answer of "not as such" probably does not make much sense. So, I'll try to explain. First, some nomenclature. When discussing angular momentum, in general, we talk about it relation to the systems axis of rotation. Since, most fermions only have two values for their spins, +/- 1/2, we think of the axis of rotation as either pointing up (clockwise rotation, or spin of +1/2), or pointing down (counter-clockwise rotation, or spin of -1/2). Until we give the "spin axis" a preferred direction, i.e. by applying a magnetic field, or perform a measurement, the choice of direction is abitrary. So, in the case of electrons in helium being in the ground state, they do not have any preferred direction other than being opposite to the other electron.

Here you are referring to an electrons energy level in the shell model which is measured in electon volts (eV). Specifically, an electron volt is defined as the energy an electron aquires as it is accelerated across a potential difference of 1 Volt. (Say that 3 times fast.)