Yes, I remember that part, but that doesn't imply she actively ordered to kill Sylvia (and even if she did, that order is outdated by now - well, at least that can be explained by the spy not getting a new briefing), the exile itself was enough. And after Sylvia got enslaved, murdering her would only draw unneeded attention from the system.
Sad to hear that. I feel several side characters deserve it more than some of the main ones. And it would probably not take much of your time to give them pat, kiss and embrace scenes if you ever decide to change your mind.
You're right, and in fact the high elf queen never did give a kill order. But the fairies know who she is, and that she's not liked by the queen. So they take it on themselves because they feel their actions will be rewarded (they won't be). Just loyalist brainwashing.
Murdering Sylvia would absolutely call unneeded attention, which is exactly why she was sent to Syl'anar on a "mission" (to never be seen again)