Tyvar's first ability doesn't grant haste to any creatures, nor does it allow you to attack with creatures as though they had haste. However, you will be able to activate abilities with in their activation costs as soon as creatures with such abilities come under your control.
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Activated abilities contain a colon. They're generally written "[Cost]: [Effect]." Some keywords are activated abilities; they have colons in their reminder text.
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For Tyvar's last ability, you may return any creature card with mana value 2 or less from your graveyard to the battlefield, even if it wasn't one of the three cards milled as the ability resolved.
You may activate abilities of creatures you control as though those creatures had haste.
+1: Untap up to one target creature.
−2: Mill three cards, then you may return a creature card with mana value 2 or less from your graveyard to the battlefield.
in their activation costs as soon as creatures with such abilities come under your control.