Disclaimer: although the theories and information I present here is as internally consistent and as canon-consistent as I can manage, it is not verified, confirmed, dispensed, or in any other way affiliated with J. K. Rowling's own explanations. The goal of this is to add my headcanon to that of others, so don't mistake this for canon truth.
Harry Potter and all affiliated characters belong solely to J. K. Rowling.
The following files were compiled by Senior Unspeakable [REDACTED]
Miscellaneous:
Frank and Alice Longbottom were tortured, but not just by the Cruciatus curse. Pain alone can't drive a person insane in the same way they are. Along with physical pain, their memories of those they loved were Obliviated. Their long-term memory became permanently and severely damaged, and they can only clearly recall a few minutes into their past, along with the pain from the Cruciatus.
Time turners have existed for at least 2500 years, but the modern ones used by the Department of Mysteries are only between 150 and 300 years old. Due to the Principle of Magical Balance, creating an object which can bend time[1] requires the death of a timeless creature, a phoenix. To make a time turner, the most recent ashes of a phoenix must be exposed to a Dementor, which will drain the phoenix's powers through the ashes. The phoenix will become a mortal diricawl, and the ashes will become the sand in the time turner. The glass of a time turner must be blood-glass, created from human blood[2] and the blood of the diricawl. Along with all this is a system of spells which must be cast in the proper order in the proper times in order to create the interwoven enchantments that allow it to function without paradox.
Albus Dumbledore learned how to cast a talking Patronus from Nicholas Flamel, who may or may not have taught others. He in turn taught the Order of the Phoenix and no one else, but Kingsley Shacklebolt made it standard for Aurors to be able to cast both a Patronus and to make it talk.
Most people believe that the Dark Arts can only do harm, and thus they are called Dark. This is false. The Dark Arts can do many good things as well as cause harm[3]. The Dark Arts are Dark because they're addictive. Casting a Dark Spell is incredibly easy, and feels good. As soon as you do it, you want to do it again. The more Dark spells you use, the more you want to use, not just the one's you've cast but others as well. So research into the Dark Arts must be undertaken very carefully in order for researchers not to become addicted.
[1] Along with taking a person back in time, a time turner is itself time-locked and nearly indestructible, and can be reshaped to be able to time-lock other things, to travel forwards in time, or to alter the flow of time for an object or person.
[2] Whoever's blood is used to create the blood-glass is the designated creator of the time turner. Only their blood can allow the blood-glass to be reshaped, as blood-glass is otherwise nearly indestructible.
[3] In fact, many advanced medical spells are derived from Dark spells. An example is Effrom's switch, a specialized switching spell made from switching skin from an animal with that of a person. Effrom used it to quickly heal the victims of whippings, swapping their skin with the skin of a pig – so he could continue whipping them. Nowadays, it's still used to heal people, but without hurting them even more afterwards.
Canon violations in this chapter: the Dark Arts are not addictive, and in fact are more difficult than normal spells. There are no other overt violations of canon, but nothing in the entire chapter is supported by canon.