It's broadly rumored among fans that the amulet-ribbon is some kind of "seal", and that taking it off will release her true power. In some doujinshi, when the amulet-ribbon is removed Rumia develops an EX form in which she looks more mature, has wings, and/or wields a giant dark sword.
Her catchphrase in fan works is そーなのかー (So- nanoka-) which is a pretty childish way of saying "Is that so~." Rumia first says this in EoSD during Reimu's scenario.
She is usually drawn with her arms spread out, claiming the pose appears to say, "The saint was crucified." Of course, this just makes her look more childish. Like Cirno, she isn't too bright.
Some people speculate that the reason why she can't take her amulet off is because she spreads her arms a lot.
In fan works, she is often seen with other lower level, childish characters such as Cirno, Mystia Lorelei, and Wriggle. Together, they are known as Team 9.
In fan works, Rumia is also a glutton and likes to eat people.