Half of the things you're asking about are actually present on the verse pages for
The Gamer, as they apply to everyone in verse, not just one specific person. You should find some of the answers you're looking for with regards to Gaia's preventative power and Illusion barriers/ID Barriers there.
Spamming fire attacks won't be too useful either unless they have some really large AoE. Kwon's entire guild uses fire attacks, and she recovered easily from the guild leader's attacks. Attacks that should've broken bones much like Kwon's do, but had practically no effect due to her regen. The reason why she has invulnerability as opposed to simply low-mid regen (Whereas Han has Low-Mid regen), is because the way its been portrayed for her is as invulnerability. Tanking attacks without flinching, such that she could, quite literally, just run or fly towards Claire, brushing off her attacks without flinching. It takes quite a lot of damage to be able to accumulate more damage than someone who's Low 7-C can, considering the fact that Claire is 8-A. Even the flames that are much stronger than her usual ones, would have to completely overwhelm this invulnerability. Which, granted, they might.
If the black flames aren't listed on her first key then I'll need to add them. Though I would hardly call having a speed advantage against someone whose entire arsenal is nothing but long ranged attacks a stomp. Considering that Kwon has no long ranged moves of her own. In particular since she doesn't start off with her black flames, and would have to decide to use them. And if Claire is as great a strategist as what's been stated/shown, that should allow her time to win. But her win condition is so much harder than Kwon's that it seems far more likely that Kwon will overwhelm her with a speed, CQC, and limited durability negation advantage.
Also, for a final note, unless the dematerialization is instant like teleportation, the cat would have to evade the punch, or kick, from Kwon. And if she's using the cat, but can't use her whips, that seems like it would put her at even more of a disadvantage.
I'll ask Risci to comment here as well. He may be of some use.