No, you cannot tap a creature with summoning sickness.
No, you cannot tap a creature with summoning sickness in Magic: The Gathering.
No, abilities that require a creature to tap or attack cannot be used if the creature has summoning sickness.
No, creature abilities do not have summoning sickness. Only creatures themselves have summoning sickness, which prevents them from attacking or using tap abilities the turn they enter the battlefield.
No, creature tokens do not have summoning sickness.
No, tap abilities do not have summoning sickness.
No, a creature with summoning sickness cannot block an opponent's creature.
Summoning Sickness stops a creature from attacking, and prevents it from tapping as the cost of an activated ability that uses the tap symbol. Non-tap abilities are not affected by summoning sickness. They can be tapped for the cost of abilities that do not use the tap symbol (such as that of Gilt-Leaf Archdruid).
No, you cannot activate a creature's ability when it has summoning sickness.
No, you cannot activate creature abilities if they have summoning sickness.
Yes, Mutavault has summoning sickness when it becomes a creature.
No, you cannot convoke a creature with summoning sickness during your turn.
Defending creatures deal damage to an attacking creature's toughness when they block equal to their power. It's called 'blocking', not 'attacking back'. Summoning sickness has no affect on blocking. Summoning sickness is the inability of a creature to use tap (tap symbol) abilities or attack until the next turn of the owner who summoned it.