The carrier is a pretty standard show of force. They won't come close to any action. It's merely there to make the North Koreans nervous (and it will). This will go the way it always does.
No. South Korea could wipe the floor with North Korea and take on a significant part of the Chinese army by themselves. With U.S. support, SK would come out on top in any conventional war.
I'm thinking more that the US would want to stay out of this conflict only because we're currently worried about Afghanistan.
The U.S. has plenty of manpower; they have a large amount located in Korea anyways. But that's not even the point. Not even one more U.S. boot has to touch Korean soil for the U.S. to wreck China/NK via air and naval power.
North Korea isn't Iraq. Of course the U.S. could do some real damage, but in the process we'd take some very real casualties. A completely different sort of hurt than the occasional F-15 pilot getting shot down over the sandbox. That's a risk that we're not even going to consider. Anti-ship missiles are very nasty business.
Manpower doesn't matter all that much in a war between two technologically advanced countries. China could have a billion soldiers and it wouldn't make a difference. The U.S. could beat them with one hand behind their back.
That's not a good way to look at it. It might be true (but I doubt it), but the cost would be very ugly. Plenty of people win fights but get the absolute living shit beat out of them in the process. Kind of a crappy tradeoff.
North Korea isn't Iraq, I agree. They've got a slightly superior air force (although probably not any better trained), but inferior equipment for the army (somehow). The major difference would be will to fight I suppose, but that's an unknown. Also, at least some of Saddam's forces were combat veterans, whereas none of NK's would be. In a conventional war, I don't believe U.S. forces would take a high rate of casualties past the first week or so. The air power factor is simply too massively on the U.S./South Korean side.
And manpower doesn't really matter in a modern war. Aircraft are too powerful, satellites are too pervasive, and weaponry is too accurate for a nation like NK to overwhelm the U.S. through numbers.