Good points raised Vienna on China dealing with Kim ala Vietnam rather than agreeing to work with the US and UN, although if the US does some economic backroom deals with China I could see them perhaps being a bit more agreeable to it than before.
However, in terms of a DPRK first strike...well, it's probably in Kims best interest not to...ok, he's not the most level headed of characters, but he's not tried invading in the last 60 years and has usually known just how far he can push it and get away with it.
You see, if the DPRK strikes first, firstly it throws away the victim card which is an important card to hold onto for propaganda on both your own citizens and those of your aggressors nation. After all, since the US lead the invasions of Iraq and Afghanistan, it would be easy to label it an 'imperialist warmonger' and gain some sympathy in peace protesters in foreign nations, particularly if you show pictures of destroyed 'baby milk factories'
But anyway, let's say that Kim does decide to throw away that card, and heads south. Well, first he's got to get across the most heavily mined and defended border in the world. Not easy. He can go under it, however the amount of troops that can go under the DMZ would be limited by the size and scope of the tunnels, and given that there is some pretty good equipment on the DMZ border for detecting earth tremors, I'd say that there aren't that many tunnels that aren't known by the ROK already, marked and probably ready to be exploded on top of any DPRK troops that mass through it.
He could try going over it, his wooden aircraft would make a low signature on the border radar systems, however again, there's the problem of numbers, most likely the AN-2s...if they can fuel enough of them...would be used for commando raids.
He could try blasting his way through, detonating a nuke under the DMZ would clear any mines and opposing forces out of the way...but then you've got only one clear exit route which would turn into Koreas own 'Hells Highway' through constant air bombardment.
Amphibious assaults around the DMZ are out of the question because the DPRKs surface navy is...lacking in the essential equipment, shall we say.
The last option is to human wave it, throw as many men as you can at it and force your way through with sheer manpower...viable, and likely to succeed but can be done only two ways. On narrow fronts, in which it incurs minimal initial casualties but then has the same problem as the nuke clearing option, or through a wide front in which high casualties are incurred but a greater section of the front smashed open.
In all scenarios, however, there is a massive loss of life on both sides in the opening stages, and that's before the ROK/US response. It is possible and likely that the DPRK can force several breaches in the DMZ, that much I will admit. However, proceeding beyond the DMZ becomes a bit more difficult. Forward units may reach Seoul, however their supply lines will be smashed to pieces by Allied air attacks and I'd estimate that the battle-line will stabilise about ten-twenty miles from Seoul.
Meanwhile inside the ROK, all hell will break loose, DPRK sleeper units will detonate bombs at army bases and airfields and inside Seoul and communications will be shot for about twenty four hours...however, the ROK and US will have been prepared for this and have secondary communications systems in place...if they're not prepared then I'd question what the US taxpayer is spending its money on TBH.
That twenty four hours of confusion will get the DPRK forces towards Seoul with high casualties along the DMZ as Allied units are overrun. However within that twenty-four hours a new defence line will be set up in front of Seoul. That line will hold, or if it doesn't the next one will. Soon the DPRK forces will find themselves low on ammunition and fuel. Small breakthroughs may occur along the defence line but the DPRK will lack the available material to exploit them because of lack of fuel and ammunition.
By this time, US reinforcements will be on the scene. DPRK subs and mini subs will try to hit the carrier fleets but most will be lost in the process, others though will be used primarily as commando landing craft, and will be hit by coastal sub-hunters.
If I had to guess...and this is pure guesswork here...I'd say that the front line will get this far:
Somewhere between the red and blue lines I'd say. I imagine Inchon would be a vital secondary target for DPRK forces because of its naval resupply ability for the Allied forces. So they'd probably make a drive south to try and get that.
So, DPRK is halted. The Allied forces are fully ready...the repulse will begin, driving the DPRK back to the DMZ...and then across it...what happens next is debatable...either a repeat of October 1950, or a collapse of the Kim regime and the appearance of a new (most likely military) leader who would sign a ceasefire and peace treaty, or the complete invasion and dismantling of the DPRK and incorporation into the ROK to become one unified Korea. It all depends on China really and the stance they take.
Either which way though, casualties will be high, but as in the last Korean war, they will be higher for the DPRK than for the Allies, and since Kim has thrown away the victim card, and hit first, public sentiment will be less against the war as it is a war of defence...although the deeper the Allies go into the DPRK the greater the call will be for them to have stopped at the DMZ and put things back into the status quo with a new leader in the DPRK. So war weariness will not be as much of a problem as it would have been if the Allies had struck first...and I'd say that Kim knows that, if he didn't know that, then he would have invaded long before now...but he knows, deep down, that he hasn't got a hope in hell of winning. So, he takes it to the edge, threatens everything under the sun, and then plays tennis with UN embargoes and the like, all the time working on the one thing that could possibly level the playing field, a nuke small enough to put on a missile and a missile system that can hit something that isn't the Pacific Ocean.