Does a melded creature remain melded when it leaves the battlefield?
From the Eldritch Moon release notes:


  While a meld card is anywhere other than the battlefield ... it has only the characteristics of its front face.


So once a melded creature is in the graveyard, the two parts have their front-face identities only and do not "remember" that they had been melded. Anything trying to move the cards back to hand or battlefield will have to interact with them separately.

However, a creature that is rescued from death with regeneration never actually leaves the battlefield at all, so regeneration works just fine on a melded creature. Regeneration does not mean to return the creature from the graveyard to the battlefield - rather it (roughly) means "the next time this creature would die, instead it doesn't."

Here's part of the Comprehensive Rules on regenerate:


  701.12a If the effect of a resolving spell or ability regenerates a permanent, it creates a replacement
  effect that protects the permanent the next time it would be destroyed this turn. In this case, 
  “Regenerate [permanent]” means “The next time [permanent] would be destroyed this turn,
  instead remove all damage marked on it and tap it. If it’s an attacking or blocking creature,
  remove it from combat.”


While the melded creature is on the battlefield it counts as just one creature, so a single regeneration effect can save it (you don't have to regenerate both halves).