Tangent: I also played Peach the most in SMB2, admittedly mostly because I was young and her float ability was the game's version of easy mode. I love that it became a consistent part of her character, though.
Regarding Toadstool vs. Peach, my Mario lore isn't exact but I think Nintendo says her full name is Princess Peach Toadstool, so Peach would be her first name. Why they switched it in translation outside of Japan at first is anybody's guess. I suppose it was just to keep with the mushroom theme (or maybe it was because peaches have certain...associations in Japanese culture). Who knows?
There's some variety in how super heroes fly. You've got Warren who's physically built for it in the most natural sense. Then you have characters like Rogue (when she's had flying powers) who just...will themselves into the air for lack of a better description (I don't know if any explanation has been given for how those forms of flying work).
Jean and Ororo are similar in ways in that their powers are keeping them aloft. For Ororo she's being held up in a way similar to a kite or hang-glider where Jean is more in a perpetual state of not-quite falling. That could be one explanation for why it took her a long time to properly fly; she probably has to concentrate a lot more than others while doing so. Even in the silver age if she was airborne (which is a bit generous considering she was usually only a couple feet off the ground), she could only maintain it for a brief period; minutes at most I think.