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:
Undying (When this creature dies, if it had no +1/+1 counters on it, return it to the battlefield under its owner's control with a +1/+1 counter on it.)
"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:
302.6. A creature’s activated ability with the tap symbol or the untap symbol in its activation cost can’t be activated unless the creature has been under its controller’s control continuously since his or her most recent turn began. A creature can’t attack unless it has been under its controller’s control continuously since his or her most recent turn began. This rule is informally called the “summoning sickness” rule.
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".