1-3: Researchers debate over this. The real answer is that, back in Gen 3, there wasn't much of a formal research community so a lot of info especially on how to "read" Gen 3 events is just gone.
Also, to the best of my knowledge, with the lack of wonder cards, there's little differentiating Gen 3 event Pokemon with regular Pokemon caught within the games.
However, if someone is offering to trade you anomgzors legit shiny Celebi, it's probably not legit.
4: Probably.