From the MTG rules:
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.
Do I correctly understand then that other abilities, such as the Gnawing Zombie's ability can be used immediately after being placed onto the battlefield?
{1}{B}, Sacrifice a creature: Target player loses 1 life and you gain 1 life.