What exactly does “rare earth” mean?
Rare Earth Elements. Not to be be confused with Rare Earth.
The rare earth elements are elements near the bottom middle of the periodic table (yttrium, erbium, etc.). Many of the strongest permanent magnets are made of various alloys of these metals. Of course, since (as the name implies) they’re somewhat rare (at least, compared to iron), rare earth magnets are more expensive than the regular kind.
The best ways I know of to separate magnets is with other magnets, or pieces of metal. Last year I had a few rare-earth magnets I bought from a surplus store (only slightly less strong than HD obtained ones), and showed my brother that they would hold each other up through the center of your hand, so don’t put them on yourself where they’d pinch you. That might have been a sadistic thing to say, but he was 20, so it was his fault when he slapped them on his ear and started yelling for me to get them off. 
IIRC I used two metal knives, one on either magnet, and fortunately the attraction between metal and magnet was greater than magnet-to-magnet through an earlobe, and he was free. I don’t guarantee that’ll work in your particular case though, so try to avoid it. 
While disruption or melting of structure can result in loss of magnetic properties,
this is not what is happening here at the Curie temperature. Magnetism is caused usually by aligned interactions of nuclear spins. As the temperature increases this allows the population of less favorable, more energetic, non-magnetic interactions to increase, until there is no net alignment. Atomic motion is not involved.
While disruption or melting of structure can result in loss of magnetic properties,
this is not what is happening here at the Curie temperature. Magnetism is caused usually by aligned interactions of nuclear spins. As the temperature increases this allows the population of less favorable, more energetic, non-magnetic interactions to increase, until there is no net alignment. Atomic motion is not involved.
A weak magnet can also be made from ordinary ferrous metal by aligning it with the Earth’s magnetic field and giving it a sharp rap on the end with a hammer. This came in handy once when I had to insert a tiny screw that was too small to hold and which kept falling out of place before I could tighten it. After I magnetized the screwdriver as described above, the screw stuck to the end of it until I tightened it in place.
By “aligning with the Earth’s magnetic field”, you just mean point it north (or south), right?
Yes.
You realize that I said this 'way back in post #3, right?
Actually, in middle latitudes like the continental United States, the Earth’s magnetic field has a strong vertical component, as well. So ideally, you’d point it north and down at some angle (very roughly 45 degrees, depending on where exactly you are). If you want to be more precise, you can use a device called a dip compass to get the exact direction.
Yes; in older hard drives, the read/write heads were scanned across the surface of the spinning platters by stepper motors, but this was too slow, so modern hard drives move the heads with a voice coil actuator; this consists of a coil of copper wire held between two magnets on a pivot bearing; when the coil is energised, it generates a magnetic field which interacts with the field from the fixed magnets and this acts to turn the pivot and move the read/wite heads. The more powerful the magnets, the more effective (and therefore rapid) the action.
I managed to get the strongest pair of my hard drive magnets apart and, holding one in my palm and placing the other on the back of my hand, they pull together with sufficient force not only to stay in position, but to feel a little uncomfortably tight. I can move paperclips with ease right through a thick wooden table.
Putting the two magnets back together is frightening; there’s no way to do it gently by hand; they will either be snatched from my grasp, or they will trap and pinch my fingertips with sufficient force to cause blood blisters.
Aha, but is is Mange Tout or Man Get Out?
Put them on opposite sides of a stack of paper, and pull the paper out one sheet at a time.
The Curie temperature is also used in the field of piezoelectric (materials that give off a voltage when pressure is applied, or change shape when a voltage is applied) materials. In piezoelectrics, the Curie temperature is the temperature at which you “depolarize” a given chunk of piezoelectric material. Similar to magnets, a piezoelectric material consists of many “domains” in the bulk material that need to be aligned in order for the material to exhibit piezoelectric properties (just like you need to subject a ferromagnetic material to a magnetic field to make it magnetic). For piezoelectrics, this is done by applying a voltage across the material (this process is caled polarization). If you bring a polarized piezoelectric above its Curie temp, it becomes depolarized (like if you drop a magnet and cause the domains to lose their alignment).
I think it would get to the point where they are gripping the paper too tightly to pull it out without tearing. If I intended to keep them as loose magnets, I’d probably knock up a hardwood wedge that I could slide them down, but I’m going to fix them to a board anyway so I can go trawling for iron micrometeorites.
Interesting, how does the third method work?
More or less. In the Northern Hemisphere, hold the bar on a tabletop pointing north, with the northern end a couple of inches above the table. I assumed that the object is align it with the “lines of force” we all saw in elementary school science books that all converge at the north magnetic poles.
Well, obviously not at the time, duh.
What does hitting it do?
It used to be that nobody knew for sure. Maybe that has changed since I retired. It appears, though, that in some materials the mechanical shock allows the elementary magnetic fields to at least partially align themselves with the incident field.
…they develop an attraction between them. What? Well, no, it rhymes with that, but the word is flux.
I have a tool used to magnetize or to demagnetize screw drivers, scribes, etc.