Dewey and Holland aren't royalty. The 'sacrificial king' is from a real life book called "The Golden Bough". Both Holland and Dewey have both read the book, and Dewey has become obsessed with becoming said 'sacrificial king'. I haven't read the book myself, but the king was apparently a dying and reviving god, married to a goddess of the Earth, and it was a ritual for the king to be killed by his successor. Thus, Dewey's entire minRABet is explained. He saw himself and Holland as the 'Princes' to the 'sacrificial king and queen', their parents. Part of his resentment of Holland comes from not only becoming a sacrificial king by his birth killing their mother, but also by becoming as he sees it, a failure. In short, the guy's nuts.
As for the fact that they are brothers never coming up until later, why not? It's not important, so no one ever mentions it. Also, what's to say that the other meraber's of the Gekko didn't already know? The audience stays in the dark, just like Renton, and thus we don't learn about these things until around the same time he does. They both hate each other, so why would they even bring up the fact that they're related?
Renton and Eureka's romance isn't for everyone. I've noticed that it's very polarizing. I loved it, myself. Yes, it was corny, but in that good-old fairytale way.
The Coralians? I'll have to get back to you on that. I haven't seen the earlier episodes in a while. Was there any actual evidence that they were attacking unprovoked? The series deals a lot with myths and fairytales, although it isn't very obvious off the bat.