Jon doesn't even make it to Hardhome in the book, we basically have no idea what happens there.
I wouldn't put much stock into any of these. There's no reason to think R'hllor actually exists, let alone a "Great Other". Mel, though she means well, also tends to be really stupid about what she sees and misinterpret things.
This isn't a Melisandre thing, this is a basic tenant of their religion. Moqorro says the same. There are not many Gods, just two. And we've seen far too much done by the various red priests (including Thoros) to doubt that something is powering their various feats.
I'm willing to bet that R'hllor and the Great Other exist, but not in a banal good vs evil kind of way. They're probably Eldrich Abominations, far beyond the understanding of mankind or the concerns of "the people", interested only in battling one another. The way the Doom of Valryia is described, it sounds like the kind of thing an angry Red God would do, no?
She's also made it "very clear" that Stannis is the chosen savior of Westeros, even when her fires keep showing Jon snow for some reason lol. I mean she thinks Bran is an agent of the Great Other too, and he almost got eaten by zombies until Jojen saved the day by exploding.
Mel's chapters reveal that despite the power given to her, she's just kinda bad at her job. She has warped all of her interpretations to fit the conclusion that Stannis is the chosen one. Benerro and Moqorro receive similar visions and they (correctly?) interpret that Azor Ahai is Dany. If the Red God doesn't exist, who is sending these visions? What is their purpose?
There also isn't a connection between "light=life" and "dark=death", which I think you're suggesting with the Faceless Men? All of Mel's magic requires death to operate properly, and making shadows ages you incredibly. Conversely Bloodraven shows the darkness can be a source of comfort, protection, and life through the use of Weirwoods. There's probably blood in there too, but it's not that black and white.
The Red Priest's powers require sacrifice, not simply death. Sacrifices of blood and fire.
Consider also, The Black Goat of Qohor is one of the many international death Gods seen as an aspect of the Many Faced God by the faceless men. The red priests tried to burn a statue of it in Qohor (revealed in AFFC). As a whole, they consider a release from the pain of the world as a gift.
I don't know where Bran and Bloodraven fit into what's going on up North, but I'm going to assume that they are trying to recreate the conditions that defeated the White Walkers in the first place. However, that's a pretty big assumption, and like Arya I'm not going to assume that Bran is being used for "good" simply because he's Bran.