Hopefully I'm not leaving anything out, because it's a confusing novel.
Pretty much all the ones she has on her profile, but also
Creation (Planned to create millions of realities, and had the power to once she absorbed the Mad Mind),
Fire Manipulation (The Doctor, whose powers run on the same source to a lesser level, burned her alive),
Reality Warping (Was fundamentally altering reality) and
Fusio (She merged with the Mad Mind). It's also possible TQA had Quantum Mnemonics (see
here for those powers) because she had access to The Mad Mind's memories, which did include Mnemonics, and heavily heavily implied she can use Block Transfer Equations, which are far inferior.
- The Quantum Archangel needed the analytical engine that was the Mad Mind to fulfil her destiny. The Lux Aeterna wanted to use it to remember and understand its existence. But Anjeliqua Whitefriar knew that a Mad Mind, resentful of its defeat at the hands of the new gods, fully in command of the reality-altering abilities granted by quantum mnemonics, would prove catastrophic for the universe. And so she had altered its memories, tweaked its perceptions. She could have altered its past, but the consequences of the Millennium War still echoed aeons later, and she couldn't yet calculate the consequences of such a change. It was true that, allied with her, it would have access to her own omniscience, but that omniscience would be under her absolute control. There was nothing to fear from the Mind of Bophemeral.
Here's The Doctor literally setting space on fire.
- 'Shut up!' A gas giant, its rings disintegrating as it was propelled through space at lightspeed, narrowly missed him. In retaliation, the Doctor set the region of space around the Quantum Archangel on fire, the quantum foam bubbling and burning. She screamed in pain ― hopefully that would weaken the Mad Mind's hold.
Here's the Quantum Archangel creating or throwing an existing black hole, and drawing in surrounding matter. For reference, they were billions of light years away from the Great Attractor, and it was Kronos who blew it up, so they're talking about a different black hole.
- The black hole exploded in the Doctor's face, momentarily blinding him. He could feel that something had broken inside him ― ribs, perhaps ― but there was no time to worry. As the Quantum Archangel got angrier, she was upping the stakes. He could sense through their shared access to the Lux Aeterna that she was reaching out to a distant nebula, drawing its matter towards her.