Honestly there’s not much that’s taught about the fall of some angels. There’s a lot of popular notions and fiction.
The angels were created good. Some chose to reject God. Their choice is irrevocable, not because God refuses to forgive them but because that’s just how angels work (it’s a mistake to think of them as disembodied human minds). If there was a war amongst angels I don’t think there’s much more to say than that. They are not human warriors fighting with weapons over land like we would imagine. Neither are they sorcerers casting fireballs at each other.
St. Thomas Aquinas put a lot of thought into angelology. To St. Thomas, goodness and the being of a thing are very close to the same thing. The better one is actually has the perfections belonging to what one is, the more good it is. Moral goodness is related to the deliberate choices we make in that regard. Anyway, the angels were created. They reflected on the knowledge they had, which was a good act and a proper action for an intellectual being. It is how they decided to act following their reflection that was good or bad.
Angels do not have bodies and so do not have senses like we do. They exist as intellects with infused knowledge. They do not think discursively (meaning it is not a piecemeal process or step by step over time like in us). They do not get hungry or sleepy. What they decide to do based on this knowledge, since they don’t flit about from thought to thought, is permanent. There is no “train of thought” in the knowing of angels.
The Catechism has a little in the following sections.
https://www.vatican.va/archive/ENG0015/__P1C.HTM (start with 391)
I don’t know how familiar you are with St. Thomas’ Summa Theologica. It can take some time to get used to. But it’s free, and in the first book of it he writes about angels.