Why a nuke? If you're going to use something explosive to collapse the well, I'm sure there are many other options available that would provide enough "oomph" to collapse that well. A "nuke" sounds like overkill and exaggeration.
That's because the anti-nuclear activists managed to turn "nuclear" into the boogeyman in the 60s and 70s. A properly sized device used five weeks ago would certainly have done less environmental damage than the amount of oil spilled so far.
Also, regardless of the explosive used, isn't there a chance it could ignite the reservoir?
As for your final point a fire needs heat, fuel and oxidiser. The oxidiser should be absent so no fire.
All that said, it's still probably not a good idea. Hopefully it doesn't become the only idea.
I have no idea if that is true; but it seemed reasonable when I read it.