Does Izayoi let Tian activate Monochrome? Probably.
Does Monochome affect Tian? Maybe. Does it destroy the Golden Gate bridge? Highly doubtful.
Does Tian have the power to one-shot Tian either way? Ken's mountain-size calculation doesn't make any sense to me. It seems to assume arbitrary sub-minute time frames (54 seconds for 10.5 kilometers and 29.5714286 seconds for 5.75 kilometers, if sheer vertical movement is being assumed, which would be another error unto itself), and doesn't explain why this particular mountain's size is relvevant to Izayoi's feats. But no matter how vague the size of the mountains, they're still mountains. Yes.
Does Tian have the power to one-shot Izayoi? Izayoi has no given sharp-resistance, so yes.
Does Tian's greater melee reach give him an advatange in scoring the vital first blow? Yes.
Will Tian utilise that melee reach effectively in-character? Probably not.
Winner:
Izayoi / Ken
It seems fairly conclusvive that Ah Gou is unlikely to open with Monochrome, and his Mutated Form's speed and durability don't seem sufficient to prevent CaoCao from stabbing him before he decides to resort to it.
Ah Gou's other options seem notably countered and nothing is really done to dispute this.
Winner:
CaoCao / Ken
If the gap in physicals between the two brothers is great enough that Huang Long would be overwhelmed, and unable to resort to lightning after engaging, in melee, his knowledge of Chi Long and motivation to win would make opening with lightning likely.
Thus, this match hinges on whether or not Chi Long can resist Huang Long's lightning in order to enforce a mostly undisputed melee win.
I don't buy that a sword being empowered with thunder has the same amperage as natural lightning, irregardless of both sharing a user. Chi Long taking damage from such a hit doesn't look good for him, either; even if he's in a stronger form in this match-up, that form having better lightning-resistance is unsubstantiated. Huang Long's lightning is presented as generally superior to natural lightning, rather than exclusively superior in terms of heat, so I see it hurting Chi Long as plausible, though Chi Long's esoteric physiology offers reasonable grounds for resistance.
However, even were Chi Long to resist Huang Long's lightning in the conventional sense, there's the supplementary argument that Huang Long's lightning conducts through Chi Long's crystal body and damages the blood he needs to live through heat. As Chi Long's given heat-resistance is the vague and external "is on fire", while Huang Long's heat output is conceded as being superior to natural lightning, I see blood-damage as a viable win condition.
Winner:
Huang Long / Verlux