1. I don't know. A block heater would probably do more good, but since you're in SC, it might not make too much of a difference.
2. Lean burn is a feature on certain engines, I know Honda and Mitsubishi have them, that basically reuses some exhaust product as gas again. Some quick definitions are available
here. It's not really a 'bolt-on' modification you can just add to your car, unless you want to swap the entire engine with a lean burn engine. Unless another model of your car had a lean-burn engine, it would be pretty difficult to add the engine, you'd have to make custom engine mounts, fit the engine to the transmission, and deal with other issues as well.
3. It will cost whatever a manual transmission, clutch pedal, shifter assembly, and some other various parts will cost you at a junkyard, eBay, or wherever else you can find them. Let's say $500 in parts, plus the time it will take you to swap the transmission, and figure out all the other electronic stuff as well....the newer the car, the harder it is, for the most part. You probably wouldn't see an overall financial gain for a while, unless you could sell the automatic parts for a decent amount. Personally, I would save the manual swap for when your automatic starts acting funky, or developing leaks, or some other reason to replace it. I'm sure that you can find a guide online for converting a Neon to a manual. Neon's are fairly common cars, and I'd be surprised if there wasn't already a guide on how to do it.
Also, what does your typical route look like? Unless you're driving highway miles, 40MPG is going to be very tough with an automatic. If you're getting 32 city, then that is very impressive, and you really should be happy with it.