1. The Creeper goes in front of you and you draw to replace. Any time you draw a Creeper it goes in front of you, even if you're drawing a card that won't go in your hand. So, for example, Dreams and Omens works that way, too.
2. If you have a doomed card, you can do it. It doesn't matter what else you have. Yes, Creepers go in front of you; see #1.
3. Put your Creepers in front of you and replace them (repeating as necessary) before anyone takes a turn.
4. One is removed. Current player decides. That is, the person who was current player when the New Rule was discarded.
5. You draw more cards, yes.