Magic The Gathering, Galvonoth/optional mana cost/Blaze/Sprout Swarm?

If i have Galvanoth (at the beginning of your upkeep, you may look at the top card of your library. If it's an instant or sorcery card, you may cast it without paying its mana cost) so lets say the card i look at is Blaze( blaze deals X damage to creature or player) and it cost X,and a red to play, if i chose to play it will it deal 0 damage or a defualt of 1 or do i get to pick and say i choose 20 and make it do 20 damage? and if Galvanoths effect i find sprout swarm which has multiple effects could i activate sprout swarm's buyback for free through Galvanoths effect or would i not be allowed to activate buyback at all because it was activated though a special circumstance?