OK, I'm going to review my thoughts on Remilia here. I might be preparing for a writeup later, though I have nothing planned yet. (With Meiling and the SDM writeups, I had the basic idea of what I was doing about a day or so in advance, although the writeups themselves were mostly on the spot)
Remilia is a selfish and vain vampire who, despite said selfishness and vanity, doesn't do anything actually evil. (In fact, the few things she does do are extremely selfish or for selfish reasons, but not actually causing anyone real harm that I know of) Perhaps because she already sees herself as on top of the world, and thus has no need to "conquer" anything? (Unless you count going to the moon as attempting to "conquer")
Her spear is apparently the mythical lance wielded by Odin. It might be just to have theme naming with Flandre's lance thing. How vampires from western Europe (or so we speculate, based on naming) could end up with Norse divine weapons is beyond me. It could mean something, it could just be rule of cool.
She apparently has every vampire weakness except crosses. To make up for cross-immunity, she also has all the oni weaknesses as well. How she manages to do anything is beyond me, but apparently she pulls it off, with (attempted) elegance and grace even. (Eastern Gensoukyou residences are not keen to Western vampire weaknesses?)
She can apparently manipulate fate, but we never see it actually used, only implied. (which raises a question, why didn't she just fatehax it so that she was destined to never be defeated during Eo SD
? Remilia doesn't seem the type to care about fair play)
She is apparently friends with Patchy, but the exact nature is unknown to me. She is at least friendly towards Meiling, but, again, exact nature unknown. She trusts and relies on Sakuya, but I think it's more "Master and Servant" than "Friends". Flandre is her sister. Exact details beyond that are clouded.
She has next to no backstory. She is the head of House Scarlet, she comes from Europe (maybe), she lies about Dracula heritage, and she wants to go outside. That's it. (Then again, Touhou doesn't have the deepest of plots, no offense.)