I believe the part two epigraphs are being written TO Hoid instead of by him.
Hoid is old, and he could be an old friend. We can assume he's essentially immortal as well - he was present when Adonalsium was shattered. And that must have been a long time ago.
In the events of Way of Kings, might Hoid be looking for this element, whatever it is, despite the fact that the author of this letter says it has a good home? Perhaps Hoid doesn't believe its home is a safe one.
For one, I don't think Hoid would call people old reptiles. We saw how eloquent he was as Wit, with those carefully-crafted insults designed to get under peoples' skins. Would someone that eloquent and masterful with his insults lower himself to call someone just an old reptile? Also, might Hoid be the one with an insistence on nonintervention? We haven't really seen him intervene in a grand way, have we?
Hoid's the one with the friends of the Seventeenth Shard, isn't he? I think 'Your friends' refers to his friends.
"Our war here." Here, as in Roshar? Could the Almighty have written this letter before he died?
But there are also a few epigraphs that make me think they're not written to Hoid. I've attempted to think of possible explanations, though.
See, I'm not sure about this one. Why would someone be telling Hoid about these people? Hoid knew them. But maybe the author if this letter (if not Hoid) knew them too and is merely mentioning them, using them as a reference to lead into the question about the stance on nonintervention.
I think Hoid would be the one to know that Aona and Skai are dead, which is a point in favor of the idea that he wrote this, instead of someone else writing it. One possible explanation to this: The beginning of that epigraph did say "In case you have turned a blind eye to that disaster", which implies that more than one person could have seen the disaster. Someone who doubts Hoid might be telling him of this, even though Hoid already knows.
I'm going to use this quote here too. We saw Hoid being searched for, chased, in the epigraph at the Purelake, which also supports the idea that Hoid is the author of this letter. But then, more than one person can be chased at a time.
I'm sure there are readers more observant than I am who can add to this on either one side or another. I just had this idea upon finishing the Way of Kings and I'm wondering what the rest of you think.