I have a wizard with 5 willpower and an encounter starts.Will my wizard start the encounter with 5 power per the rules for equilibrium?Is my wizard able to cast a spell with cost 3 without gathering power first ?Is the same applied to Piests?

Yes. You start encounters at Equilibrium Power/Favors (unless special circumstances, like you cast a spell / invoke a Blessing that starts the encounter, or GM's evil touch)