Phyrexian Furnace
1, Artifact

: Remove the bottom card of target player's graveyard from the game.

,Sacrifice Phyrexian Furnace: Remove target card in a graveyard from the game and draw a card.
1st question:
Is it possible to activate Phyrexian Furnace (especially the second ability) when there are no cards in any graveyard? Do I get to draw a card?
2nd question:
Do I get to draw a card, if I activate the second ability and the targetted card is removed in response?