In a nutshell, everything that happened in the first three episodes was a troll. Yes, it was all faked - for the benefit of both the audience and the major characters. I don't think it took a genius to figure out Prince was up to something, but to carry this farce off the extent that manga-ka Yoshihiro Togashi did takes some real balls. The entire three-episode arc was a ruse cooked up the Prince - the amnesia, the crash, the cat, the fight - every damn speck of it. And the willing dupes (besides us) were Yokitaka, Edogawa, the Captain and his men. Supposedly this was the test the loyalty of his men, but Prince's real reason appears to have been boredom - apparently he's a super-intelligent brat who spends his intellectual resources exclusively on elaborate practical jokes. Oh, the Disckonians were in on the joke - they agreed to help Prince in return for the chance to observe Yukitaka, since they're huge baseball fans and most of the strong baseball areas are controlled by the Ellerians.
It takes real courage to play that game of chicken, to carry the gag all the way to the edge and then keep going - most writers would have chickened out far earlier. But it was the completeness of it that makes it work. Playing jokes on an audience doesn't always go ever well, but the fact that the clues were all there and almost every character got trolled too makes it enjoyable instead of infuriating. And this show really knows how to do comedy - the retrospective film the Prince made covering the whole ruse from start to finish was a classic.
So now what? Well, we have a time skip to three months later - and Yukitaka and Edogawa get a letter from Prince saying that he made a glorious success of the Galactic Conference. Not only that but he made the Earth part of his domain and he needs to move there to keep an eye on it. But the PV shows neither hide nor hair of any of the characters we've gotten to know so far - what's the deal there? That could be a troll too, or a side story - the manga readers know of course, but I don't so no answers here. I can't imagine we've seen the last of the Prince and Yukitaka but maybe things are going episodic from this point and we'll leave them for a while.