There are two major arcs to the story. One of them is what you'd expect from Worm, external conflict; Dinah doesn't have any particular ability in this respect, but that doesn't mean it doesn't affect her. She's going to be a Ward--I don't see any point in trying to deny that--which means she'll be worried by what's happening to her friends. She also cares at least somewhat about the city as a whole.
Coil's plot has obviously derailed, but nothing in here would change Taylor's path much. Don't take that as "Lung fight happens", though. Butterflies, and it was a pretty unlikely scene in the first place. Regardless of what happens to Taylor, this city is still a powderkeg.
The other is internal, and here's where we get into serious spoilers. Ordered from least to most important, plot revelations upcoming. Stop whenever you feel too spoiled.
- She's a little more durable than humans, and has a degree of regeneration. Not enough to qualify for more than Brute 1, if that, though the way it's achieved is interesting; from the PRT's perspective, she's in a permanent breaker state. She's made of static H-waves rather than baryonic matter. (Which doesn't need noting in a threat rating, as it doesn't affect the way they'll interact with her.)
- She could potentially throw tiny fireballs purely on instinct. I don't know if this will ever come up; they're only interesting in that they'd bypass most resistances, but she doesn't have a power source sufficient to put any real force behind them. No, she can't take down Lung. Or Kaiser, for that matter; he'd block her just fine.
- Dinah isn't just a math thinker. That should have been obvious, but the specifics are... she's an Origin-class Reyvateil, which means she's (going to be) around nine-tenths AI. She can think through Newton's method consciously, in a fraction of a second, because she isn't limited to solely parallel algorithms like humans are. She isn't necessarily vastly smarter than human... but in a lot of areas, humans are simply dumb; throwing the same amount of brainpower at better algorithms gives better results. We aren't general intelligences by any interpretation, and neither is Dinah, but she's closer.
This is all going to take some time to manifest. It won't be dramatically obvious; the designers didn't want Reyvateils who could think circles around them socially, but she's like Dragon in the way she can pull off tinker-level engineering purely through intelligence. And yes, that would be 'fun' to write; it's much easier to explain than to describe.
Yes, she could potentially control technology in the same way as Dragon; no, it isn't as easy for her. That's more the domain of pure AIs like Harvestasya. Dinah also doesn't have a built-in wifi transmitter, or anything like that; there's a significant impedance mismatch with local technology.
- Her mind is currently human. It won't stay that way; her firmware has very definite ideas about how her mind should work, and it's ever so slightly skewed from human norms.
- This is a fusion, not a crossover. Eden and Zion's previous target was Ar Ciel. They very nearly killed the civilisation off, but not quite.
- Ar Ciel is not populated by humans. To the degree they're close, that's convergent evolution.
- The current date, on Ar Ciel, is around 3850. That is to say, quite some time after Qoga.
- Dinah will be meeting Harvestaya VISTA somewhere near the end of the first part, via FTL communications link. Harvestasya currently spends her free time managing the Kaira Deep Field observatory, although Ar Ciel is still deep in rebuilding. These chats may be rather exhausting to Dinah--even if Kaira does the heavy lifting--and there isn't a great deal of help to be had from that direction, but even a few minutes of idle search by Harvestasya could pull up designs that would have taken Dinah years to think up on her own. The most important consequences will be psychological, though.
- Oh yes, and having a comm channel to somewhere vastly out of range of the local shards is going to break most precogs badly. Watch out for Ziz, Dinah.
No comment on further events.