The creatures the bugs mentioned in the song (the hen who lays exploding eggs, the creature with 49 heads, etc), do they really exist in-universe?
From what's implied, yes.
In the film version, how did Aunt Spiker and Sponge get to the US from England? Now there's not a lot of idea of how long James and his friends travel for, but the aunts show up in a waterlogged car, suggesting they drove through the ocean or something. Given they told James off for dreaming up "impossible things", it's hard to not see that as contradictory.
Spike and Sponge being hypocritical wouldn't be out of character for them. They're fine with "impossible things" so long as they get to do it and James stays miserable.
During the climax, once James stands up to his aunts and Sponge and Spiker grab fire axes to kill him, why don't the police try to restrain them, especially the officer who protected James since his arrival? All that the cops do is ask the onlookers to stay back, turning their backs on a situation that could have possibly ended with James’s death had the insects not arrived to rescue him.
The fridge page answers this one in that it was a safety measure. They were trying to get the onlookers out of the way to minimize collateral damage before they started shooting the aunts.
Why would James be placed in the custody of his arrogant aunts in the first place after his parents died? Did James had no other living relatives left? It's not been said in either the book nor movie (well, technically I've seen the movie but never read the book and the wiki didn't say either).
The book makes no mention of any other relatives other than Spiker and Sponge.
Rhinoceroses in real-life are herbivorous, but it’s said here that James's parents were eaten by one that escaped from the London Zoo. How is that even possible for a rhino to eat two full-grown humans?
It's one of those absurd plot points that Roald Dahl does. At least the movie rectifies that in some form by having the rhino be a demonic cloud.
