On the Death card it says you can remove it when it stands alone. So my question is, As soon as I draw it and it stands alone can I remove it right then, or do I have to wait till my next turn to discard it?
I disagree with the other answer.
The card text says:
This card has two effects:
I believe the second is the effect you are asking about. That means that if, at any point during anyone's turn, that is the only card you have in play, you may discard it. To answer your specific scenario. If you draw it (and automatically play it) and it is the only card in front of you, you can discard it immediately.
You can discard it at any point during your turn, if it is alone at the end of the draw
The rules text on the Death Creeper card says (emphasis mine):
The Rules state under the On Your Turn: box, "Optional actions allowed by New Rules, Keepkers, etc may be performed at any point during this sequence." The Death Creeper's last ability, may be performed at any point during your turn. (With a minor exception mentioned in the Creeper Rules when drawing multiple cards, "You might have to accept several Creepers at once as you draw cards, until you've drawn the required number of non-Creepers and added them to your hand.")
Also from the FAQ, you cannot take any actions during other players turns, so anytime isn't as often as you think.