Why does an aircraft usually go nose-down at low to medium airspeed, but goes nose up when the pilot performs a high-speed dive? It would appear that the Horizontal stabilizer's pitching torque would somehow grow faster with airspeed than the main wing's pitching torque. Why would that be? Could it be that the flow becomes more turbulent with high-speed and that it would affect the surfaces with the greatest area more than the ones with less area? Aircraft usually have their CG ahead of the Center of Lift, don't they?

More airspeed= more lift.  The plane will "want" to make the dive more shallow, trying to rise above your intended glidepath. I don't think the nose is pitching up so much as it takes more forward pressure to keep the nose ponted at the target point below the horizon.
  This is one of the reasons that the preferred method of extreme diving in fighters is to roll over, then drop almost straight down, nose low but inverted. Any additional force required to keep the dive steep (and much less should be required) will result in a positive load, whereas if you're diving "rightside up", as you push the nose down, you're adding a negative load. Most planes tolerate much higher positive loads than negative ones.

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Other than damage, ice,  or failure of control surfaces, there's really only the kind of "reversal" that sometimes happens with ailerons. I... need to look that up; it's hard to explain. Hmmm...
Let's say you're flying at a high angle of attack for your desired airspeed, and although the wing hasn't stalled yet, it's very close. You decide to bank without letting the nose down for some reason, and as the aileron comes down on the wing you're trying to raise, it changes the angle of attack  (remember that's relative to the airflow over the wing) of that area of the wing, sending it past that critical number. That wingtip stalls, and no matter how much you try to lift that wing, down it will go. The effect is that you, say, turn the yoke to the right, and the plane rolls left. Probably into a spin if you're really not paying attention, as the other wing comes up and that tip stalls, then the whole wing, with the plane in a knife-edge attitude.
Most planes nowadays have sufficient "washout" (change in chord angle from root to tip; makes the wing look "twisted") to compensate for that effect, but it's still possible.... especially at high speeds. I've heard of it happening while inverted, such as in an outside loop.  Unless the wing has a symmetrical cross-section and almost no dihedral, the angle of attack upside-down is going to be quite different.
The other, more common cause of control reversal is mechanics rigging the cables wrong... that's why "controls free and correct" is a very important checklist item.