The Witch of Izalith didn't create Pyromancy. As stated on the Izalith Catalyst, originally the Witch and her daughters used Flame Sorcery. It wasn't until the Flame of Chaos was created that Quelana created Pyromancy, which drew its power from nature rather the self.
Also, we don't know for sure that Anor Londo was built during the War. It could have easily been built afterwards while the Gods were settling down after their victory.
Woahwoahwoahwoah. Solaire is by no means confirmed to be the First Born/God of War.
Gwyndolin was raised as a woman because, traditionally, lunar powers and the moon itself are considered feminine. It wasn't out of shame, it was just because "the moon = feminine."
There is nothing concrete whatsoever that connects Seath to Gwynevere. Or even Priscilla.
A bit of my own speculation, but I always figured the Darksign was a long-term plan by the Pygmy to usurp the Gods of Light. Being the only soul of Darkness, it quietly hid away until the light began to fade, and once that happened it would resurface to overthrow the now-weakened Gods of Light. The Darksign was simply the "call-to-arms" for potential candidates who could inherit the Dark Soul once the plan was finally set in motion.
While it's possible, it's never said that Gwyn asked the Witch of Izalith to create another First Flame. She could have also decided that all on her own either as a bid for more power to overtake Gwyn's spot as leader of the Gods or out of desperation as of the theory you state in the OP.
Remind me again where exactly the game says that Havel tried to fight Seath, or that Gwyn gave the order for Seath to steal maidens?
Wasn't Artorias's sword cursed when he himself became consumed by the Abyss? I don't remember it saying that he made a contract with the darkness.
While not directly stated, based on its description Gough's Helmet being blinded is implied to have been done from within Gwyn's army rather than by Oolacile residents. It makes it seem like it was a kind of racism against Giants in that they were looked down upon by "normal" Gods and Demigods (what I call things like the Silver Knights) as mindless brutes, and the idea that one of them could become a high-ranking knight was some kind of offensive notion among them.
You left out Seath on the list of people Gwyn gave parts of his Soul to.
While not really direct lore and more of a personal thing, you seem to be cutting Smough short. It's implied that he would have been able to be one of the Four Knights if not for his personality, but that aside his strength alone made him garner respect from much of Gwyn's army. If not from Gwyn's army in general then at least from Ornstein (who's implied to be the second-highest ranked member of the army after Gwyn himself). I never really saw Smough as a monster. More like Ornstein's lapdog.