Power Null just works. She sees the magic they are using, and just stops it working. Or forces it to work the wrong way sometimes, causing them to immolate themselves and stuff.
Her existence erasing black flames spawn at the location she wants them to. She normally does it with a finger click for style, but she doesn't have to.
Possession - she's basically an angry invisibile intangible ghost. There was a litle interaction with the world, like the classic spooky wind and angry screech, but other than that, no she can't do anything while she's a ghost except possess people. She can only possess Sensitives (psychics), or a clone of her self or something similar. If it's not a clone though, she can't use magic and is weakened to the possessed body's level, and the body will burn out in a few hours due to being unable to handle her soul's power. Then she can possess someone else.
She resists this, she doesn't have it (well, sorta. Her ability to perceive magic lets her know what magicians are going to do with their magic by sensing it). Like I said, sensitives are psychics. When they were trying to observe her, in present or future, they would either get nothing at all, black out and go unconscious or would go brain dead.
She doesn't have Power Drain, she resists it. There's this thing called the Cube that was used to hold Argeddion, who is another sorcerer who discovered his true name and gained access to true magic. He's comparable (though slightly weaker) to her in power, but is vastly more experienced and knowledgeable. She also killed him and absorbed his knowledge and power. The Cube basically drains their power, and then uses it to fuel a spell to keep them asleep. She stated that even putting her in the Cube would not contain her.
Soul Manipulation - she does have this, but she also resists it. Feats of using it:
1. Ripped a Remnant out of Tanith Low. Remnants are evil souls that possess others and merge with their souls. After 4 days of possession, the soul integration is complete, and the Remnant and the original soul have become one, and are thought impossible to separate. Tanith had a remnant in her for years. Darquesse separated the Remnant from Tanith anyway.
2. She can kill and absorb Remnants, gaining their energy and power.
3. She was also able to mess with Skulduggery's soul, and in the vision pulled his soul apart (this part of the vision was only a few minutes of vision-time after she was put under, so it's very likely something she can do)
4. Considering her necromancy, power mimicry and how often she's seen and observed the workings of the Death Bubble, she can likely use it too. It expands from the user extremely quickly, bypasses forcefields and when it retracts it rips the soul out of any living being within the bubble.
Feats of resisting it:
1. Nye seals her soul from outside control.
2. Casually brushes off the Death Bubble from Lord Vile, which is implied to be strong enough to rip out the souls of half the planet at once.
3. Resists possession of every Remnant. There are thousands of Remnants, and like I said each merges with the soul. She had thousands of them in her at once, all actively trying to control her, and she resisted it, killed them and absorbed them to grow stronger. Also, during this feat she was extremely weakened due to having boosted Lord Vile and boosted Melancholia beating on her repeatedly.