For some reason, Lunasa is often addressed as 「ルナ姉」 or "Luna-nee."
Merlin has a bug in her programming in Perfect Cherry Blossom that sometimes causes her to behave improperly during the sisters' final spell card. As a result fans have portrayed her as being occasionally rebellious or even crazy.
A mutation of a computer-programming meme on the Japanese message board 2ch called ぬるぽ or "Nurupo" (short for "Null Pointer Exception", which basically means "Disregard everything I just said") resulted in someone changing it to めるぽ or "Merupo". This almost immediately became a popular nickname for Merlin, although it could also be described as her alter ego.
Merupo is depicted by replacing Merlin's head with a smiling Shift_JIS head with a squiggle of hair down one side of its face, like so: ξ・∀・）. As far as Merupo's personality goes, think Merlin, only twice as stupid and twice as crazy (the only word Merupo seems to be able to say is her name).
Merlin has a great tendency of being drawn with a larger chest in fanart, perhaps because of the remarks in PMiSS about her being the tallest and most eye catching, similar to Komachi
There are a lot of fan art where Lunasa is holding the violin wrong, Merlin is playing the trumpet with her ear and Lyrica is palming the keyboard. However this doesn't make fans believe the sisters are stupid because they can still play the instruments without any contact anyway.