The answer to all of those is “yes,” because it triggers from that 2/2 creature dying. Then the trigger asks if you want to pay 3 life or let the card return to its owner’s hand. No matter what types the card has, since it was the creature that died while it was face-down, it will be the card that can return to its owner’s hand.
The plus side here is that you get to see what the card is before you decide, since it was revealed and will be face up in the graveyard. For example, if the card was a Shock, you may decide that it’s better for the opponent to have that card that only deals 2 damage rather than paying 3 life to keep it in the grave.
Today’s Rules Tip written by Josh Stansfield