I've been wanting to make a list of all of the way magic is used in the series like how there was one for the clothing
Hierarchs: The Voice (needs an expositor to work), whatever was going on with Raihankana (they were the hierarch's voice and it seemed like the hierarch possessed them or something), cannot have their life drained by demons (based on Highsun at the end of Book 2)
Intentions/expositors' designs: water multiplication (cageling court), fire (Kai, different ones for the fire in his hand, the bridge burning one, and the one from the beginning of Book 2 (I think this last one was the bridge burning one just with limitations)), heatless fire (Kai), amalgams (expositors, creates false life that cannot be drained by demons), will imposition (Aclines), suspension (Book 1 Ch 2), stasis (used to knock out Ziede in Book 1 Ch 13 and then Kai used it to knock out someone else, may have been what was used on Ziede in the tomb and the boat crew at the beginning of Book 1), defensive (Book 1 Ch 4, what they do is not specified), monitoring (Book 1 Ch 5), following (Aclines with Tenes' help, used to follow the hunter-beast (an amalgam I think)), life stealing prevention (Cantenios, used against Kai but they didn't work, Book 1 past timeline), alerting (summer halls expositors, Book 1 past timeline), sealing (expositors), demon-killing (put onto cursebreakers, doesn't kill demons immediately, presumably a weaker form of this intention exists for the cursebreakers that just knock out demons), light and shadow (Kai, Book 1 Ch 13), freezing (Book 1 Ch 13), pearl hearing (Arnsterath/her familiar, uses blood in order to hear the communication in the heart pearl(s) of the person whose blood was used), demon power suppression (expositors, used to transport demons to the cageling court), pain, confusion (Kai, will leave the person extremely confused for a whole day, Book 2), death, body damaging (Kai, Kai says it would turn a mortal's guts to liquid and it caused the legs and lower torso of an amalgam to collapse, Book 2), bone shattering (Kai, Book 2), light (Book 2), trapping (Book 2)
Cantrips: flower choking (Tenes), witch cells + witch cell breaking (Book 1), smoke net (Kai, needed smoke veil/air spirits, Book 1 Ch 4), sealing off areas (Kai, Book 1 Ch 5), messenger calling (Kai but seems to have been made by the Enalin, uses birds (or possibly any animal since Kai seems to have gotten his response from a fish or something) to send messages (doesn't work on sea birds because Enalin is landlocked, Book 1), finding (Ziede, uses spit and blood, told her about entities nearby (like the body-stealing ghoul)), limitation (Book 1 past time, mentioned by Ziede who suggested Kai might be able to combine them with his intentions), easing pain (Amabel's family, Book 2), finding lost objects (Amabel's family, Book 2), choking on dust (dust witches), heart stopping (dust witches), chimeras (Kai made one out of mist and the scent from the garden, doesn't really work if someone is actively looking for intruders), thorny vine trap (dust witches)
Spirits: flying (wind, Ziede), smoke veil (wind, Ziede, needs smoke/ash to already be there), air bubble (wind, Ziede, underwater summer halls Book 1 and mountain collapse Book 2), location knowledge (wind, Ziede tasted the wind to figure out where they were, Book 1 Ch 2), messing with intentions (wind, used by Ziede to get around the alert intentions summer halls and though doors locked with intentions), moving earth (earth, Tenes), swift-travelling (air and earth, Amabel, seems to be a very rare ability), stone breaking (earth, Tenes)
Demons: life stealing (possible to use on other demons but depends on the strength of their will(?), they gain this power when they come to the mortal world, Note: seems to be possible for people to do this to a person they've taken as a familiar (Aclines did this to Tenes)), body possession, life giving? (fountain scene in Book 1, not totally confirmed but it did work on the leaf), accelerated healing (draws on their original body (stated that it's because they are malleable in the underearth I'm pretty sure), works even if their original body dies but they feel pain more sharply if their original body dies)
Immortal Blessed: underwater breathing device, communication device (goes on ear), flying boats, teleportation stone things, weaker drill thing (Book 2, getting back into the mountain), stronger drill thing (Book 2, caused the mountain collapse), laser beam thing (at least that's how I picture it) (Book 1 Ch 14, uses debilitating force, can kill a mortal if directed at them for too long, no known intentions or cantrips can stop it), laser gun thing (used by Highsun against Tahren, made Tahren stop breathing but would presumably do worse to a mortal, Book 2 Ch 10)
Other/Unsure: storm making (Ziede, Book 1 Ch 3, presumably wind-devils), finding stones (used by expositors (usually) to find Immortal Blessed), controlling someone with your will (can be used by demons, witches, and expositors; seems to be stronger the closer you are to being full demon (i.e. the Doyen) but not totally sure), making familiars (Tenes was under an intention but it may be possible to do it with your will (I'm assuming that's how Arnsterath did it but I can't tell if she took the body of an expositor or not)), creating expositors (hierarchs), memory wiping (expositors (Aclines did it to Tenes), presumably others can do it as well (since Kai and Ziede couldn't remember how they ended up in the tomb and Ziede didn't even die)), heart pearls (witches and presumably also demons can do this, may kill a mortal to have one but it might only be an issue if its grinded up before they ingest it), sending your spirit into the underearth (can be done by witches and demons whose underearth bodies have died (otherwise the demon could swap between the bodies easily) (must be done at a conduit I think)), boat spirit thing (Kai; combination cantrip and intention; used blood, spit, and the mud the barge was in), finding intention/witch work (done by Menlas, Kai was unsure if that was how he and Ziede were found, Book 1 Ch 2), sealing entrances (Ziede, unclear if it's a cantrip or spirits, Book 1 past timeline), rumor that the hierarchs could use birds and spirits like spies (Book 1 past timeline), portents (Mother Hiraga), wind calming (Amabel's family, presumably air spirits, Book 2), finding water (Amabel's family, presumably water spirits, Book 2), dust cloud (dust witches), disrupting communication with spirits (dust witches, done to Ziede), weird decay tentacles (dust witches, used against Kai, beginning of book 2)
Cantrips don't work in water but intentions do (Book 1 Ch 13)
Demons can survive having a weapon in their heart (at least for a certain amount of time) (Book 1 Ch 13)
Immortal Blessed are harder for demons to drain than even powerful expositors (Book 1 Ch 13)
Demons have a stronger sense of smell (Ex. Arnsterath finding Ziede's blood in Book 1, Kai smelling intentions in Book 1, Kai smelling Bashat's suppressed anger in Book 2)
Kai mentioned being able to taste expositor's power (Book 1 past timeline)
Witches see the world as the movement of energies
Demons seem to still be able to use their previous body's abilities even after moving onto a new body (i.e. Kai can still use intentions even after he's in his present body which presumably isn't an expositor)
Kai wrote the Saredi word for "reveal" on the deck in his blood (Book 1 Ch 5) in order to anchor himself and make it easier to navigate the expositor's intention
The Tescai-Lin reincarnates (does not seem to be common knowledge outside of the Enalin (there was some note/letter/article where someone was wondering if they were elected or born into the position) and unclear if it's common knowledge among the Enalin)
Using a wells power may tell other people with a connection to the well where you are (speculated by Kai in the Book 1 past timeline)
Intentions are easier to keep in reserve than cantrips (at least for Kai they are, Book 2)
Convincing spirits to do their bidding drains witches and it's worse if they have to force the spirits (Book 2)
Other creatures: wraithlings (Book 1, can be communicated with from the underearth), imps (Kai summons these for light (pretty sure they're from the underearth)), soul-stealer ghosts (Book 1), bone-eating vines (Book 1, not sure if this counts as a creature but it sounded interesting), body-stealing ghouls (Book 1, can keep body parts from spoiling , Note: the hierarchs' "homegrown monsters" being worse than stuff from the underearth is mentioned in this section so either Kai saying these monsters are from the upper earth or he's saying the hierarchs made them), bear-people Liberni (Book 1, all we know is that they hibernate in caves near where the Saredi lived, presumably not (very) hostile as Kai and Adeni were mentioned to have explored the caves)
Changes that happen if a demon's original body dies (Book 1): loss of much of their night vision, tire more easily, need to eat more, and feel pain more sharply
Also can someone tell me if it's mentioned if Kai heals slower after Enna dies
Also also let me know if I got any of this wrong so that I can fix it and please add anything I missed in the comments