R: After you draw this card in your opening hand of a game, you and your opponent each lose 5 vitality. This card remains in your card pool intil the end of first turn.

is this supposed to be "THE first turn" or "YOUR first turn"?

if the oppenent goes first do i leave this in my card pool or do i get to clear it at their end phase?

If I am correct, the reading says "Until the end of First Turn" So I will go with the choice of it meaning until the end of your first turn.

The first turn is the first turn whether you play said first turn or your opponent does... but that text would be totally irrelevant if it didn't work the way Itachi Uchiha said (so, stamp).