I'm sorry, but this info is nearly ten years out-of-date. First, the Gutmann method was designed for encodings back in the days of RLL/MFM encoded drives. For newer drives which really push the physics quite a lot further, two passes of random data are enough to throw the magnetic domains into a statistical dead heat. There just isn't any physical room on the drive to hold old data.
Secondly, new drives reserve a percentage of the room (invisible to the user), in case some of the sectors go bad the controller will re-map them transparently to new sectors. This might leave old data in the old sectors, where you can't normally see it but an investigator armed with the proper ATA commands can. (This isn't a conspiracy of the government and drive manufacturers, it's all there in the ATA spec.) The correct way to securely erase a drive is to send the drive the SECURITY-ERASE command. The drive controller will securely erase every part of the drive. https://ata.wiki.kernel.org/index.php/ATA_Secure_Erase The NSA actually recommends this to other government agencies, so it's probably OK.
You don't know, you hardly ever know anything. You evaluate the evidence (as laid out by the GP) and conclude that it's most likely the case.
This is really the approach that most conspiracy theories take. The fact that we don't know something to be true (but it's very likely to be) is used as an implication that it's probably false.
If that possibility seriously concerns you, follow it up by physical destruction of the drive. Magnets strong enough to actually damage the data aren't a good cost/benefit from what I gather (too strong, too dangerous, too much hassle), so either shred or melt the drive platters.
I'm generally satisfied with df if=/dev/zero of=/dev/sda because I'm not actually dealing with anything that sensitive, but if you are, just take appropriate steps. Defense in depth.
It doesn't concern me that much, but I'd rather fill the drive with random data myself first. I can do the ATA-erase thing afterwards.
On a related note, I also have zero trust in manufacturer-supplied encryption that sits in the drives. There is no way for me to verify whether it actually does anything.
I think that incinerating the disk should erase the data. Magnetic material become normal materials after some temperature http://en.wikipedia.org/wiki/Curie_temperature . Usually it is no more than 1000 C/ 1800 F, so a good fire should be enough.
Well, you don't know. It all depends on what kind of data was on the target drive.
If it's schoolwork or unimportant business data, a format is good enough. If we're talking CC and SSN numbers, the ATA command with writing 0's is good. If it's sensitive, a sledgehammer and an anvil is suitable.
I inherited a junk 1G hard drive, and just 'filed it away' in my junk drawer. After years, I actually checked the contents. Lo and behold: a flat database full of medical data, including SSN's and other revealing data. It was only 1G so it got the sledge (I use a small section of railroad tie instead of a blacksmiths anvil).
Secondly, new drives reserve a percentage of the room (invisible to the user), in case some of the sectors go bad the controller will re-map them transparently to new sectors. This might leave old data in the old sectors, where you can't normally see it but an investigator armed with the proper ATA commands can. (This isn't a conspiracy of the government and drive manufacturers, it's all there in the ATA spec.) The correct way to securely erase a drive is to send the drive the SECURITY-ERASE command. The drive controller will securely erase every part of the drive. https://ata.wiki.kernel.org/index.php/ATA_Secure_Erase The NSA actually recommends this to other government agencies, so it's probably OK.