When you play the seaway you put you +buy token on a card. What happens if it is a duration card. Do you get the +buy for the turns while it is in play or just the turn you play it?
Just the turn you play it. The official rules state "Four tokens give +1 of something: +1 Action, +1 Buy, +1 Card, +$1. These tokens go on Action Supply piles. When the player whose token it is plays a card from that pile, that player first gets the bonus."
So, when you play a card with the +buy token, or any of the other vanilla bonus tokens, you first get +buy,
then you do whatever the card says, which includes the duration effect if it's a duration card