Energy expert: Nuking oil leak ‘only thing we can do’

A "properly sized" conventional explosive would be impractically enormous: nukes are measured in kiloton or megaton yields. There is no way to effectively detonate (say) twenty million pounds of conventional explosives all at once, never mind the non-trivial challenge of emplacing that amount. As I understand it, you'd place it below the sea floor, into the well, so the surrounding water would be shielded by all the rock above the blast site. For the same reason, there would be no fallout plumes, because all that solid mass would prevent the newly-created radioactive material from going anywhere. And it can't ignite the reservoir, because there's no oxygen to burn down there.

All that said, it's still probably not a good idea. Hopefully it doesn't become the only idea.

My understanding was the explosive was going to be put down the well or buried in a second well close to the leaking well. Nuclear bombs are more compact, for equivalent yield, than chemical explosives which is why I assumed they were being proposed.

As for your final point a fire needs heat, fuel and oxidiser. The oxidiser should be absent so no fire.

Conventional explosives require oxygen to burn, this things a mile under water, it ain't going to happen. Nukes don't require oxygen.

Not a problem for two reasons: 1. Oil won't burn without oxygen. It might break up into simpler hydrocarbons (carbon dioxide, methane, etc.), but it won't cause a firestorm. 2. Burning the oil is much less bad than letting it leak all over the coastline, poisoning animals and preventing oxygen from getting mixed into the water. There are already several operations intentionally burning the oil on the surface.