The way to evolve Haunter has been, and will always be, by trading. If you have a Haunter in Pokemon Emerald trade it to Sapphire, Ruby, Fire Red or Leaf Green and make sure he isn't holding an EVERSTONE as that will prevent its evolution.
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You can't catch a Haunter in Emerald. You can trade for one, you can find a Duskull/Dusclops at MT Pyre, but you can't straight out find a wild Haunter.
No you must trade from FireRed and LeafGreen
yes into a haunter and the trade it to evolve into a gengar
Yes, Haunter is a very good Pokemon
Haunter evolves when traded