Total cost is the printed cost on the resonator card. It is equal to the number of colored will plus the number of colorless will listed on the card.
Valentina's activated ability can be countered by "Glimpse of Kaguya," but the resonator itself cannot be countered (by "Xeex, the Ancient Magic," for example) if put into play through her ability. If her ability is countered by Glimpse, the resonator is not revealed from hand.
Valentina's activated ability is optional. You can choose not to place a water resonator into play upon resolution of the ability if you wish.
If Valentina steals an attacking or blocking resonator with her God's Art, it ceases to be an attacking or blocking resonator. If the stolen resonator was attacking, the battle will end, and if the stolen resonator was blocking, the damage from the attacker will go through to the original attacked object.