All elves hated Sauron because Sauron was a Maiar who supported Morgoth and commanded his armies. Morgoth (and a big spider called Ungoliant) destroyed the 2 trees of night and day and then stole the silmaris. The elves have been at war with Morgoth since then. Thousands of Galadrials people have been killed by the armies of Morgoth.
This is why she hates Sauron.
And yes her brother was killed by a werewolf or something. Werewolves are like wargs and i'm not sure on the difference tbh.
Werewolves were one of Sauron's corruptions though.
Sauron does trick the elves into forging the rings though. Way more to it than pretending to be a king that knows what an alloy is.
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From @jiherio