Magnet to wipe HDD
That won't work. You'll need to degauss it, which will render the drive unusable.
Sure. Get a powerful magnet, put it next to the hard drive, with N facing the drive. Then flip it around so S faces the drive. Then flip it again, then again. Do this a few thousand times a second. If you do it any slower or just put it near the drive once, you'll just cause the bits on the platter to move a little. That will, of course, prevent the head from reading it, but it will not prevent expert forensic recovery. You will need to flip the magnet back and forth thousands of times a second to truly scramble the bits such that their patterns are completely dissociated from the place they started.
Does shaking the magnet that fast sound too hard? Well, luckily there's a method to avoid having to do it that fast, called degaussing. Degaussing is the process of using an electromagnet to generate a powerful alternating magnetic field to completely wipe a hard drive. It is one of the only methods which is generally agreed upon to obliterate all data present on a drive.
The reason that an alternating magnetic field is required involves the physics behind magnetics. It's the change in the magnetic field which transfers energy, not the magnetic field itself. Just like gravity, the mere presence of magnetism does not provide energy. This is the reason why a generator requires magnets moving around coils constantly, rather than simply being in close proximity to magnets. Now what does this have to do with flipping bits? Well, when you put the magnet near the hard drive, the act of moving it near causes some bits to move, but holding it there for a long time does little else. If you flip it around, the bits will move like crazy, being pulled by the changing field, because the change is what is providing the energy to flip bits. A human can't move a magnet enough times to reliably change all bits, but a powerful electromagnet with an alternating current can, as each switch in polarity gives out more energy.
Note that doing this will break a hard drive, and render it unusable. And I don't just mean the head will be damaged (although it will), but the guide tracks on the platter which were put there when it was manufactured, and which were never meant to be removed, will be erased as well. So no, it will not be possible to use it as if it were brand new. Degaussing will both damage the precision electronics, and erase the guide tracks which the head needs to operate. It's simply safer and more cost-effective data destruction method than the competing and equally effective method: phase transition, or literally vaporizing the hard drive itself. It also lets you recycle the materials.
You may be interested in this fun Defcon talk on hard drive destruction. They tried out various popular methods and showed which ones were and were not effective. It may surprise you (hint: thermite and drills are overrated).
Not without opening the hard drive. This magnet reseller tried several magnets on a running hard drive, without any bad results.
It would also probably not securely delete your data when holding magnets directly to the platter, altough it may flip some bits.