Cancel Affinity & Falchion/Breath of Fog

Nope, Cancel Affinity just "cancels" color advantage, not weapon.

Cancel Affinity 3 reverses the enemy's Triangle Adept/Gem weapon, it has no effect on weapon effectiveness (Falchion, Poison Dagger, etc). Standard triangle advantage/disadvantage is 20%.

With CA3 against an enemy that uses TA or a gem weapon, they would be considered neutral (20% advantage - 20% from reversed TA/GW = 0%)

No, cancel affinity only works on, well, color affinity advantage.
Weapons are effective, so that's another thing altogether.

No it’s just take avantage on the colors but it helps anyway one day I face a Nowi anti advantage with Deirdre and .... that's not good for my poor lady of the forest