If you target yourself, this spell has no useful effect. It will not cause an infinite loop since a replacement effect can’t modify the same event more than once. This effect will not modify the draw that it has you perform.

If you and your opponent each cast Plagiarize on each other during the same turn, the two spells effectively cancel each other out. You will draw cards when you normally would and so will your opponent.

You draw the card from your library as normal, not from your opponent’s library.

If you target a player whose library is empty, any effect or turn-based action that would cause that player to draw a card will cause you to draw a card instead. It doesn’t matter that the other player would be unable to draw.