Valtiel and PH are angels sent from the Orders god to ensure the rebirth of their god.
Uh, no. Big ol' Triangle Head isn't an angel sent by the Orders god to ensure the rebirth of the God (how does the Order's god even send an angel to ensure it's own
birth?) PH is merely a manifestation serving different purposes depending on what game/movie you're speaking of. According to Silent Hill 2's character designer Takayoshi Sato, Pyramid Head appears as a "distorted memory of the executioners" and of the town's past as a place of execution.
In SH2 and HC, Bogeyman is the warden and executioner. He teaches the protagonist that they need to face what they have truly done. Bogeyman's name, according to the Order ,is Lamnaetal.
Silent Hill 2 and Homecoming do not share the same creature, though they do go by the same appearance. James' Red Pyramid Thing
is distinctly different from Homecoming's Bogeyman
: they come from different manifestations of different minds, and as such, are not the same being.
They aren't based on an unmentioned entity in the Order's mythology, nor are they the physical form of said hypothetical entity itself. I don't know who the hell Lamnaetal is. He isn't even mentioned in the games.
Lamnaetal and Valtiel are, essentially, Metatron's caretakers, ensuring that heather is able to birth their god. In HC, Lamnaetal is their to cause Alex to lose hope in stopping the Order, ensuring that they will, once again, be reunited with their god.
(Regarding "Lamnaetal": see above. You are correct about Valtiel's role, though.)
No, Bogeyman ("Lamnaetal"?) in Homecoming is a manifestation from Adam's guilty conscience. You could say that, similar to Red Pyramid Thing, Bogeyman serves the same purpose of representing a desire for punishment.