What happens when you discard a creature(with Undying) from your hand to the graveyard? Does it go to the Battlefield (without summoning sickness)?
And what happens if I use Mulch and put all Undying creatures in the graveyard? The same?
The fine print on the cards tell us what we need to know:
"Dies" refers to "goes to the graveyard from the battlefield." Thus, a creature card that is placed into the graveyard from any other zone doesn't trigger undying.
Since Undying doesn't say anything specific about "summoning sickness" or haste, the regular rules apply. Namely:
It doesn't matter where the creature came from: if it didn't start the turn no the field under your control, it still has "summoning sickness".