In regards to the hair colors, how come the other two princesses had Earth-style hair colors at the end of the last episode when they went back to Earth? If it takes a while for the effect to happen, shouldn't they have still had their bright hair colors upon initially arriving on Earth?

It probably happened, but we’re going straight forward to the concert : we don’t show how they find their earth-like outfits, neither when Talia / Iris teach them the basics about earth, things like that, even though it probably happened too. It’s also very likely that Talia knows a spell to speed up the “camouflage” of the hair, to be more earthlike too. :)

(Link here for the rest of the explanation about the hair color rules in LoliRock)