I dont even think if you detonated the entire worlds arsenal of nukes at the bottom of the Mariana Trench it would breach to the mantel. You're talking huge numbers. Gigatonnes of force at work.
Yeah, basing my estimate off the
Mariana Trench Explosion What-if XKCD figures I'd estimate you would probably be needing something like a million nukes before you even reached the "mass extinction" level, let alone the planet cracker level. (Though you would cause horrible hurricanes with even 1 nuke.
On moon nukes:
I'm not quite sure I agree with your numbers there. When I run the numbers I'm getting about 3.8*10^28 J for the kinetic energy, only about 2/3rds of what you are getting. Cut that down to the only 96% of the energy needed to cause a decaying orbit (as opposed to trying to stop it dead), and assuming half-megaton bombs as you did (which should release a total of 2.1*10^15 J each, assuming you somehow directed 100% of that into stopping the moon), I'm only getting a total of 1.737*10^13 bombs, about 1.7
billion times the amount the US currently has (and that's including a rough estimate of all nukes currently scheduled to be dismantled in the count).
Of course at that point if you wanted to destroy the world you could just glass the surface. A halfmegaton bomb gives us a fireball size of 882473 m^2 (thanks to
this helpful site). Assuming we were able to channel the explosions into a better shape then circles, we could glass the entire surface of the planet (land and water) with only about 577 million bombs evenly spaced out. That's only like 24,000 times the worldwide total (once again estimating in decommissioned by not yet destroyed nukes).
Carrying this with some (very) rough estimates about yield, etc., I'm guessing the current nuclear stockpile plus retired weapons could probably glass about 1 ten millionth of a percent of the land area of the earth, or about 3030 square miles (about double the size of rhode island).