During the fifth book, the Golden Trio plus Neville, Luna, and Ginny travel to the Department of Mysteries. During that time we see a variety of interesting things (Ex. the veil, prophecies, brains). Is anything known about those or other experiments? I would prefer canon based answers. I could not find an answer on Pottermore but if you can please leave a link to the article!
Yes - we know they’ve studied how certain people get magic.
Dumbledore mentions in his notes on “Babbitty Rabbitty and her Cackling Stump” that the Department of Mysteries has studied how wizards get magic, and whether Muggles can ‘acquire’ it.
“As intensive studies in the Department of Mysteries demonstrated as far back as 1672, wizards and witches are born, not created. While the “rogue” ability to perform magic sometimes appears in those of apparent non-magical descent (though several later studies have suggested that there will have been a witch or wizard somewhere on the family tree), Muggles cannot perform magic. The best — or worst — they could hope for are random and uncontrollable effects generated by a genuine magical wand, which, as an instrument through which magic is supposed to be channeled, sometimes holds residual power, which it may discharge at odd moments — see also the notes on wandlore for “The Tale of the Three Brothers.”
- The Tales of Beedle the Bard
According to Luna Lovegood in Order of the Phoenix:
And of course he uses the Department of Mysteries to develop terrible poisons, which he feeds secretly to anybody who disagrees with him.
According to Ron in Order of the Phoenix, no one really knows:
“I know they call the people who work in there ‘Unspeakables,’ ” said Ron, frowning. “Because no one really seems to know what they do in there... Weird place to have a weapon ...”
Ron's view is confirmed by his father at the Quidditch World Cup:
“That was Cuthbert Mockridge, Head of the Goblin Liaison Office. ... Here comes Gilbert Wimple; he’s with the Committee on Experimental Charms; he’s had those horns for awhile now. ... Hello, Arnie ... Arnold Peasegood, he’s an Obliviator — member of the Accidental Magic Reversal Squad, you know. ... and that’s Bode and Croaker ... they’re Unspeakables. ...”
“From the Department of Mysteries, top secret, no idea what they get up to. ...”
At the end of Order of the Phoenix Dumbledore tells us one of the most mysterious things studied there:
“There is a room in the Department of Mysteries,” interrupted Dumbledore, “that is kept locked at all times. It contains a force that is at once more wonderful and more terrible than death, than human intelligence, than forces of nature. It is also, perhaps, the most mysterious of the many subjects for study that reside there. It is the power held within that room that you possess in such quantities and which Voldemort has not at all. That power took you to save Sirius tonight. That power also saved you from possession by Voldemort, because he could not bear to reside in a body so full of the force he detests. In the end, it mattered not that you could not close your mind. It was your heart that saved you.”
In Deathly Hallows they apparently studied how people obtain magic, but given the circumstances the study might not have been pure:
“ ‘Recent research undertaken by the Department of Mysteries reveals that magic can only be passed from person to person when Wizards reproduce. Where no proven Wizarding ancestry exists, therefore, the so- called Muggle-born is likely to have obtained magical power by theft or force.