its true that a Rook could fit better, but due to her bloodline and being the first piece Zeke wanted her to be a queen
Hecate's personality is the same as Asuna? well I had an other picture once but that one got broken and I was forced to pick a new one
the bow is a sacred gear, in the show there have been more holy type gears, I dont want to give spoilers but 
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Kiba's gear creates demonic swords and there is a holy version of it as well
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it wont hurt the user though, and the normal arrows are not holy at all, only the balance breaker is and same story, it wont hit the user, but due to its powers Yumi wont like to use it at all and thus starts creating the sub-species balance breaker mode

just replying to your comments ^^
also for the bow, remember a gear is often granted to a human / half human person by complete random, I mean a half vampire might just as easy get a holy longiuse gear or an half angel can just as easy get a demonic gear
then again, that was explained in the lightnovel how its all randomly granted by god's systems, dont remember if the manga/ anime were so clear on its randomness