14. "Why does my brother (older) always tells me not to bring magnets near a computer? It is because of the concept of eddy currents?"

Your brother is right in thinking that waving a magnet around in the vicinity of a computer could do some permanent damage! However, I don't think that eddy currents are his major concern. I think there are three possible problem areas:

[1] First, the monitor operates like a TV, i.e., there is a beam of electrons that flashes up and down and across the screen ... in fact, three beams of electrons are required, from three different and independently controlled electron guns, in order to produce the large variety of colors we observe; one beam for red color, one beam for green color and one beam for blue color. The inside of the screen of the monitor - and of a color TV - is coated with thousands of tiny, tiny dots of phosphor. Some dots emit red light when an electron beam hits them, some dots emit green light and others emit blue light ... the eye "sees" the light coming from a combination of these dots (and red-green-blue light can produce all the different colors depending on their relative intensities). The electron beams are directed at these dots through holes in a metal mask (called a shadow mask). The three beams traveling at three slightly different angles pass through the holes in the mask and strike the screen at the positions of the corresponding phosphor dots, as shown below.

Since each beam can only strike the dots of one color, each beam controls the brightness of one of the three colors. As you can imagine everything has to be very carefully aligned and masked inside the tube so that the beam controlling the red color strikes only the red phosphor dots, the beam controlling the green color strikes only the green phosphor dots and the beam controlling the blue color strikes only the red phosphor dots. If you bring a magnet near a monitor, the electron beams will experience a force that deflects the beams from their intended paths. As a result, the image on the screen will be distorted and have the "wrong" colors! You might think that removing the magnet will remove the force and so everything returns to what it was before. Unfortunately, often what happens is the very proximity of the magnet causes some parts of the monitor (or TV) tube to become magnetized so that a remnant or residual magnetic field exists even after the magnet is removed. So, the effect becomes, in a sense, permanent. It may be possible to "repair" the damage but it involves de-magnetizing the tube, a costly and not always successful endeavor.

As an aside, the dot pitch of a monitor is the distance between the holes on the shadow mask (in millimeters). The larger the dot pitch the more "grainy" the image on the screen. Good quality monitors typically have a dot pitch from 0.25mm to 0.30mm. In contrast, a typical TV is from 0.51mm to 1mm on projection screen TV's. That's why the picture on a monitor looks much "crisper" and "sharper" than on a TV. It also means one can obtain a much higher resolution, i.e., fine detail, which is often measured in dots per inch (dpi), using a monitor than using a TV. The "Trinitron" tubes made by Sony use a set of closely spaced parallel wires instead of a shadow mask. However, the principle is very similar. You can further information about monitors from How Computer Monitors Work.

[2] The second problem involves the hard drive and any floppy/ZIP disks that you may be using when a magnet is brought near. A hard disk and a floppy disk both operate in a similar way to regular recording tape. That is, there is a recording surface that consists of a thin plastic layer filled with (very small, elongated) magnetic particles; in a hard disk, this layer rests on an ultra-smooth aluminum disk, and in a floppy disk the magnetic layer is fixed to both sides of a stiff plastic disk. In each case, the magnetic layer passes very close to a stationary recording head that writes bits (0's and 1's) into the magnetic layer. This is done by a strong magnetic field, produced by an electric current passing through a coil in the head, which can magnetize a small group of particles in one direction - interpreted as a "0" - or in the opposite direction - interpreted as a "1"^*.

^* Each particle acts like a small permanent magnet with a N-pole at one end and a S-pole at the other. During recording, the magnetic field is sufficiently large it can interchange the poles if necessary.