1) You get your Seize the Day extra turn, then the rounds of extra turns due to Fleet start (including yours at the end).
2) Let's assume the turn that would have ended the game (without Fleet) is a normal turn, from player X (I'm not sure how it works if that turn was an extra turn). Then all remaining non-Fleet extra turns happen (like in your first example for Seize the Day), then the round of extra Fleet turns happens, starting with the player to the left of player X, and going in turn order until it reaches player X, who has the last turn.
Of course, each player only gets an extra turn if they had actually bought Fleet when that "last except for Fleet turn" of player X was over.
In your second example, I assume no Seize the Day, just you and your opponent, both having bought Fleet earlier. If you "end the game" (except for Fleet), then your opponent gets his Fleet turn first, then you get your Fleet turn second, then the game really ends.