An ICBM could carry a payload that big, yes. Are you suggesting that the missiles in your scan are ICBM's? They are clearly cruise missiles.
You're partly right, the concussive force is not radiation but the heat is. Heat is thermal radiation.
The set up says that Magneto detects the Enterprise first and they only notice him when he flies toward them. I don't know if Magneto can fly in space, but it's in the set up so I'm giving him that. There is nothing arbitrary about the fact that Magneto is generating a powerful energy field. He is using his powers to fly.
I appreciate the research you did on looking up the Enterprise phaser data. Unfortunately, the numbers from your sources are nonsense, as should be evident from the fact that they are wildly inconsistent with each other. All of them are flatly contradicted by the evidence from the shows and movies. I'll take them one at a time.
The 40 megawatt figure from Battle Lines is equal to 40 megajoules/sec. This means that a 1 second burst would have the same force as the explosion of slightly over 19 lbs. of TNT, roughly the power of a sidewinder missile.
The 1.02 gigawatt figure from the TNG Tech Manual would equal about 485 lbs of TNT, or about the power of one 18" cannon from a WW-2 era battleship.
The 4.2 gigawatt figure is equal to a little under a ton of TNT. That's roughly 1/11 the power of the largest conventional bomb.
The 400 gigawatt figure is a little more realistic, it has the power of neatly 100 tons of TNT. That's 9 times bigger than the biggest conventional bomb, but still much smaller than the yield of even a suitcase nuke.
The 790 Terawatt figure from the DS-9 Tech Manual is better, but still only yields 189 kilotons of energy, a little short of what you'd get from the warhead on a tomahawk cruise missile.
If any of these numbers made sense, I'd agree that Magneto would win pretty decisively. Unfortunately, they don't. I did some math with the 790 Terawatt output. If you put an engine with that capacity in a ship the size of Kirk's Enterprise, it would take more than 56 hours to accelerate to .9 sublight. Since we've seen the ship do this sort of thing in mere seconds, the number in the manual has to be much too low.
The other thing about the numbers that is an issue is visual evidence. Ship's Phasers and photon torpedoes visually do similar damage. Torpedo damage seems maybe slightly greater. That can't be if the torpedoes (whose explosive force can be accurately be determined based on real world physics) are many hunderds of times more powerful. The logical conclusion is that the phaser banks on Kirk's Enterprise have an out put in tho 200-250 petawatt range.
Magneto has the raw power to vaporize pieces of the ship's hull, I agree, but has he ever used his power in that way? I can't see how magnetism would be as useful in trying to vaporize something as a different form of energy, like heat.
If, as you suggest, Magneto can simply bypass the shields and directly affect the magnetic fields within the ship, he could win. For one thing, the antimatter in the ships engines is held within a magnetic field. Mess with that and the whole thing goes boom!
It depends on how Magneto's powers work. If he, or the magnetic field he generates, has to be in contact with another magnetic field in order to manipulate it, the deflectors will stop him. If he can psychically sieze controls of a remote magnetic field without such contact, he can win. We know from TNG that deflector shields do not block telepathy. If Magneto is using a similar psychic power to access the fields in the ship, the shields won't stop him. I would like to see some confirmation that this is how his powers work before I agree.
Magneto could destroy the photon torpedoes once they left protection of the shields. The fact that they use antimatter in a magnetic containment field would make that fairly simple. The two issues he'd have to deal with are range and speed. He wants to be far away from the torpedoes when they explode, but he also needs to be close enough to the ship to see (or sense) them fire. I can't find a listing for how fast the torpedoes are but I'm guessing high sublight (they are warp capable, but that shouldn't come into play in this fight.) He has good potential to defend against them, but it's dangerous, even for him. Phasers will be much more difficult for him to deal with.
Power to power, Magneto doesn't have a chance. If he can mess with the engine core, and do it so quickly that they don't get off even one phaser shot, he can win (though it's unlikely he will survive the explosion.)
If he could get on board, Magneto could easily take over the ship. In the battle as outlines, the best he can hope for is mutually assurred destruction.