Such an explosion when directed at the right place can put the asteroid off-orbit thus preventing the collision. If one doesn't help then send another.
Perhaps. But from what I've read it seems that a braking technique or slow acceleration technique is less costly and more predictable in outcome.
Give this report to Congress a quick read; specifically the paragraphs under the heading 'Precision Matters'.
Essentially, the report acknowledges the utility of using a nuclear explosion to change the orbit, but suggests that there are better tool in our kit already.