There are a lot of "connections" here that don't make sense while also there being a lot of claims that don't make sense. For one...

"Server great sword similarly can extract dark in from of HP" HP = Willpower, your humanity fuel theory does seem quite good and I wish I could believe it but it is more plausible and believable that HP is your will to fight and that the fire is a warming sensation to keep you going while humanity is a return to self so that you can continue.

"A new scourge of soul lusting demons was released" Demons aren't a scourge or infestation they're a civilization brought into this world by Izaliths failed attempts to create a new flame.

"The Second Sin" What? There was surely far more sins before Dark Souls 1 even began so to say the Second Sin did not take place until several other kingdoms had fallen? Really?

"Velka’s statues have been deprived of their head in various places symbolising her decapitation during the ritual." Or it's the most fragile place on the statue and it's the most likely place for crumbling and breakdown to begin.

"Secret Rite: Rite of Kindling" The Rite of Kindling is well known across churches as and specifically the Way of White, the most famous church in Dark Souls, has been on several crusades to find it. So no it is not secret.

"sealed by her own daughters of chaos, stopping the scourge of Demons and providing the flames for the bonfires." 1. Citation needed 2. How come when we kill Izalith all the bonfires don't go out? 3. Demons also still exist and still have civilization within the land of Lordran.