1. They need to fire them on multiple accounts, but that one is the top of my list. Well, that and their entire image of Hades.
3. Granted, mortals see what mortals want to see, but this movie is supposed to be from Percy's point of view. He would see it for what it is, which the majority would be more equivalent to purgatory than Hell. Plus how can you have them go through the main entrance into the Underworld and not have Cerberus involved? He's kinda hard to miss.
5. Ok, they so don't look like that either. At least ours don't. They're just large mastiff looking dogs with red eyes who can shadow travel. Not... whatever those were.