This replacement effect replaces the draw, so nothing that triggers on a draw will trigger.

If you use this on a multi-card draw, each replaced draw is handled separately. In other words, you reveal and then put on the bottom of the library for the first card, then do the same for the second, and so on. In a multi-card draw you do not have to choose how many of those draws will be replaced before you do any drawing or use of this card.

If no card of the chosen type is found before your library empties, you don't get a card, but you do get to order all the cards in your library any way you choose.

If your library is empty, Abundance can prevent you from losing the game for being unable to draw a card. If an effect or turn-based action would cause you to draw a card, you can replace that draw with Abundance's replacement effect. (It doesn't matter that you'd be unable to actually draw a card.) Since Abundance's effect has you put a card into your hand instead of drawing a card, you'll never be forced to draw a card with an empty library.