Good question. Maybe they did it deliberately to make it feel more alien and strange? Or maybe there's another rule about the relative number of syllables (e.g., Tom and Jerry, Jak and Daxter, etc.)

That sounds normal when flipped to me. Swapping Rick and Morty for Morty and Rick sounds wrong but Mindy and Mork still has that right to it. I think they did it on purpose.

This is likely because of the different sound profile(not sure if this is the right word) of the words. Mork ends with a guttural letter that opens up for usage of a relatively open vowel like the "a" in "and". Also, it's one syllable, and it should be easier to start with the lower number of syllables and work your way up or at least keep it that count. Mindy, on the other hand, has those two syllables, and ends with a vowel that also I believe, making this up on the spot, shouldn't open up for possibilities to follow up, which I think is why there's not just barely quite as much usage for "y" as a vowel too. Add to that that saying "Mork and Mindy" makes ylu naturally slide "O-Æ-I-I'", gradually opening up. Instead, saying "Mindy and Mork" will make you rather awkwardly jump around less open vowels: it's stressing your mouth to close more. If you say it like "Mindy 'n Mark" it should be a slight bit easier to say. Finally, and is atonal, I believe, correct me if I'm wrong, and saying "Mork and Mindy" allows Mork to quickly slide to Mindy by merging "and" with "Mork", whereas Mindy would force you to either pronounce a hiatus, or a glottal stop, forcing you to tonalize "and", which is suboptimal. There's many different rules at play than I-A-O. Why did I invest my time making a point through potentially incorrect information.