do all fuchsia blood have a horrorterror as their lusus?

with feferi she has Gl'bgolyb and i wanna know if thats like a constant with all the other fuchsia blood thats been introduced, since i know that theres one in hiveswap but ive never gotten the chance to actually playing the game (spoilers about the fuchsia blood is fine tho given the topic of discussion)

follow up to that tho is this: is it necessary for all violet bloods to feed said fuchsia blood's lusus to keep it quiet? or can it be anyone who's closet to the fuchsia blood to take on that role/ can the fuschia blood do that role themselves?