To fly into Mexico you HAVE to have a passport. As of right now the only way you can get into Mexico without a passport is by land travel, but that will change as of Summer 2009. As of Summer 2009 you will need a passport for any land travel into Mexico and Canada.
Yes. You only ever need a passport to leave the country. A passport has nothing to do with geography or transport, only politics. You can go anywhere within Canada without a Canadian passport. Or any passport for that matter.
When flying within the United States, no passport is required. Anyone can fly out of state without the need to show a passport, though they will need some form of valid photo ID to be able to board the plane.
No, you can never fly red eye without ID. The only persons that are able to fly without an ID are minor children under the age of 18. Each airline will have specific items that they will accept for ID such as a passport or state ID.