There is an event where you can catch Deoxys, Lugia, Ho-Oh, Mew and either Latias or Latios depending on what color you chose. I believe you can only do this after you beat the Elite Four. Mew is at Faraway Island. Latias or Latios is at the Southern Island.( depending on what color you chose after beating the Elite Four) Deoxys is at Birth Island. And Lugia and Ho-Oh are at Navel Rock. Good luck.
yes you can
Event
Not at all mew is an event Pokemon for Pokemon emerald.
YES, Using a Pokemon event
in lilycove
GAME SHARK!!!!!!!!!!!!!!!!!!
If you got the Birth Island event then you can get it.
catch a Nintendo event
You can only get it by Mystery Event.
Cheat or Nintendo Event
No.
I think you can't catch Ho-oh in Pokemon Emerald. But, you can find it in Nintendo event, or use GameShark...