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Tasigur's last ability doesn't target any card or player. You choose an opponent as the ability resolves and that player chooses a nonland card after you put the top two cards of your library into your graveyard.
The chosen opponent can choose any nonland card in your graveyard, not just one of the cards that was just put there.
Delve doesn't change a spell's mana cost or mana value. For example, Treasure Cruise's mana value is 8 even if you exiled three cards to cast it.
Because delve isn't an alternative cost, it can be used in conjunction with alternative costs, such as flashback. It can also be used to pay for additional costs that include generic mana.
The chosen opponent can choose any nonland card in your graveyard, not just one of the milled cards.
Tasigur's last ability doesn't target any card or player. You choose an opponent and that player chooses a nonland card only after you mill two cards.
You can exile cards to pay only for generic mana, and you can't exile more cards than the generic mana requirement of a spell with delve. For example, you can't exile more than seven cards from your graveyard to cast Treasure Cruise unless an effect has increased its cost.
