Yeah, I generally agree with all of your points. There's certainly context to explain why he acts how he does--he's in a fraught state in general (recall that in the middle of all these events, he calls his father, who refuses to believe it and instead verbally abuses and basically disowns him). Also, he doesn't really know what the MC is like or how the hotel is currently run--all he knows is that the last Master kicked everyone out violently. So it's understandable that he acts alone to find the feather--he's hopeful about the hotel, but he doesn't have reason to trust the current hotel management, so better to rely on himself. Then he sees what he believes is the same snake that prompted Clement's breakdown just casually wandering the hallways, and by the time he confronts Asterion, he's just Done With It All.
Now, to be clear, I said that the context helps *explain* his behavior--it doesn't excuse it. He's still responsible for his own actions (except perhaps when there's a smell of rotting flowers in the air...). His actions are *understandable*, but that doesn't mean they're appropriate or justified.
And that's fine--good, in fact, in a work of fiction. A character can be capable of good (see: interactions with Oscar), but also be far from perfect. And that makes them more interesting.
(Re: point 1, I very much doubt Pedro knew that it was a shrine to Hermes--he just knew it was a creepy cavelike room in the sub-basement.)