To the death and yeah.
Icon's feats suggest that while he is near Superman-level strength-wise, he is not equal to him (especially in durability), and he has also been ko'd by the Blood Syndicate before. DCU Captain Atom does have super-speed, and Icon has not exhibited Flash-level superspeed, either. Any version of Captain Atom wins this. The new 52 version is close to a curbstomp, IMHO.
I don't think it is close, at all. Captain Atom is far more powerful than Icon. Atom wins this with ease.
I don't think so.
Superman said that Icon hit him the hardest he's ever been hit. Captain Atom doesn't really have feats to contend with that. Unless it's New-52 Captain Atom. Who's faster, and a helluva lot more powerful.
Any version of Captain Atom would be able to handle and absorb Icon's energy attacks, so Icon's energy powers aren't a threat to him at all. In contrast, Captain Atom can easily generate sufficient power to kill Icon, especially since this is a fight to the death. In addition, Captain Atom does have some impressive durability feats, having been pounded on repeatedly by Maul, survived an attack by Apollo while battling near the Sun, pounding Majestic into the ground and simply getting up after crashing into a building from falling from outer space on Wildstorm Earth. Icon was once KO'd by the Blood Syndicate and none of them are even class 100. He also admitted to BogeyMan that he wore body armor for additional protection. Icon's durability isn't sufficient to survive a fight to the death with Captain Atom. Icon will lose to any version of Captain Atom.