You can obtain a Mew by getting a Mystery Gift
Sorry but you cant get mew in heart gold,so I doubt you could get 'rare mew'.
no
curmen cave
Mew can't be catched in Pokemon heartgold, only mewtwo.
Mew is only available through Pokemon Events.
you can trade
you have to have a action replay
in heart gold mew is in the Mt. Plateado if you look for moltres behind is mew or in soul silver is behind mewtwo in Cueva Celeste
you can't unless you go to a event or have action replay
i dont think there is mewthree
on may 5 Th there will be a mew event for mystery gift wifi. [ONLY WORKS FOR SOUL SILVER]