If a replacement effect would try to replace a card that you can't draw, that effect can't apply.

You can draw a maximum of one card on each player's turn. Subsequent card draws are ignored.

If you haven't drawn any cards in a turn, and a spell or ability would cause you to draw multiple cards, you'll just draw one card.

If you draw a card, and then Spirit of the Labyrinth enters the battlefield, you won't be able to draw more cards that turn.