2) I highly recommend AGAINST cutting ground anywhere near high-speed signals. Stray capacitance really doesn't have too much of an effect on digital electronics. Usually stray capacitance kills you when it acts to create a parasitic filter at the input of an op amp.
In fact, it is highly recommended to run your high-speed signals directly overtop of an unbroken ground plane; this is called a "microstrip". The reason is that high frequency current follows the path of least inductance. With a ground plane, this path will be a mirror image of the signal trace. This minimizes the size of the loop, which in turn minimizes radiated EMI.
A very striking example of this can be seen on Dr. Howard Johnson's web site. See figures 8 and 9 for an example of high-frequency current taking the path of least inductance. (in case you didn't know, Dr. Johnson is an authority on signal integrity, author of the much lauded "High-Speed Digital Design: A Handbook of Black Magic")
It's important to note that any cuts in the ground plane underneath one of these high-speed digital signals will increase the size of the loop because the return current must take a detour around your cutout, which leads to increased emissions as well. You want a totally unbroken plane underneath all your digital signals. It's also important to note that the power plane is also a reference plane just like the ground plane, and from a high-frequency perspective these two planes are connected via bypass capacitors, so you can consider a high-frequency return current to "jump" planes near the caps.
3) If you have a good ground plane, there's pretty much no reason to use a guard trace. The exception would be the op amp I mentioned earlier, because you may have cut the ground plane underneath it. But you still need to worry about the parasitic capacitance of a guard trace. Once again, Dr. Johnson is here to help with pretty pictures.
4.1) I believe that multiple small vias will have better inductance properties since they are in parallel, versus one large via taking up approximately the same amount of space. Unfortunately I cannot remember what I read that led me to believe this. I think it's because inductance of a via is linearly inversely proportional to radius, but the area of the via is quadratically directly proportional to the radius. (source: Dr. Johnson again) Make the via radius 2x bigger, and it has half the inductance but takes up 4x as much area.
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As others said, it's mostly because it was easier to manufacture than solid layers for various reasons.
They also can be used in certain situations where you need controlled impedance on a very thin board. The traces width needed to get 'normal' impedances on such a thin board would be ridiculously narrow but the cross hatching changes the impedance characteristics on adjacent layers to allow wider traces for a given impedance.
If for some reason you need to do this, you can only route controlled impedance traces at 45 deg to the hatch pattern. This approach greatly increases mutual inductance between signals and consequently, cross-talk. Also note that this only works when the size of the hatch is much less than the length of the signal's rise time, this normally correlates to the frequency of the digital signals in question. As such, as frequency increases you reach a point where the hatch pattern would have to be so tightly spaced that you lose any benefit vs a solid plane.
In summary: Never use a cross hatched ground plane, unless you're stuck in some really weird situation. Modern PCB construction and assembly techniques no longer require it.