the swashbuckler wins a battle at the oasis, and the second card allows him to teleport to another space. he does, and draws another enemy. he fights and wins, but still only gets one extra turn because of the restriction on his ability to one extra turn gained per turn. now he takes his extra turn. if he battles and wins, can he gain an extra turn, since this is a seperate turn?

FAQ, page 6:

"The Swashbuckler’s special ability should read “You
may only do this once per round” instead of “once per turn.”"

Round being 1 turn by each character.