Also covered in in-game lore. The DC-area muties were created locally and have no ties at all to the West Coast or Chicago-area bunch. More specifically, they [spoiler:ee0e76b241]were created by a particular experimental Vault program which was set up to infect humans with FEV under controlled circumstances. The mutants have actually taken over that Vault and have been kidnapping humans in order to make more of themselves.[/spoiler:ee0e76b241]
So far as the Bomb goes, recall that you aren't putting an
explosive charge on the thing...you're using a pulse generator designed to set off the bomb's internal detonator. Burke makes a point of saying it was expressly built for this purpose. Now, that's kind of an interesting point, being that
no one in the Capital Wasteland has that kind of high-tech knowhow short of the Brotherhood or Enclave --- with the possible exception of the Commonwealth's surviving MIT labs.
The Brotherhood would be diametrically opposed to doing the deed; not even the Outcasts would appear to support nuking Megaton. The Enclave's Colonel Autumn might consider blowing the bomb to be a worthwhile means of eliminating a possible major center of resistance to the planned annexation of the DC Wasteland, but President Eden would probably not be interested in that sort of move (being more focused on seizing Project Purity, and achieving his aims that way).
But the Commonwealth, blow up a major regional rival which they consider inhabited by a bunch of Neanderthalic throwbacks anyways? Oh yes. I can see them trying to pull that.
As for Tenpenny himself, he seems largely clueless as to what Mr. Burke is actually up to and appears to be more concerned with aesthetics in general than anything else. He bears no animosity towards Megaton save that it sits within view of his penthouse balcony and looks rather scruffy. So Burke, apparently acting as a free-agent in Tenpenny's name and using his resources, makes bank from the Commonwealth, and gets some other poor schlub (you) to do the dirty work.
Getting back to the Bomb itself, who says it's necessarily Chinese? Lore makes clear that once the nukes started flying, everyone chipped in. It could just as easily be a Russian device that was flown by Bear bomber (or the equivalent) over the Arctic to strike the Eastern Seaboard. There would have been a wave of those, if not several waves...the likelihood of at least a single dud out of all the strikes would have been high.
Also, two hundred years is a long time for radioactive material to decay --- and it will decay. Half-life is not something one can simply arrest; and if you could, the bomb wouldn't be radioactive. The blast is going to be much weaker than one would expect from such a large bomb simply because there's not as much useful fissionable material left in it. That said, yeah, nuclear explosions are REALLY underpowered in this game (blast radii are small, Fat Men can't even kill the Behemoths, etc).
Finally, note that there are plenty of areas around the DC Wasteland where craters show actual nuke detonations having gone off --- none of which are particularly huge. But then again, in real life, a one-megaton blast leaves a crater "only" about 1000 feet across (
http://www.pbs.org/wgbh/amex/bomb/sfeature/1mtblast.html). This seems to be largely in line with the bigger craters found in-game.
In this context, it looks like the Megaton Bomb was originally intended to destroy a major local airport --- the one nearby, that gets plundered for building materials later by survivors. A bomb intended to detonate on impact with runway tarmac, instead hitting a soft-dirt area nearby --- possibly landfill? --- might have failed to detonate simply because it missed its target.