Could a Nuclear war actually crack the planet in two?

Answer 1

No.

• There are not enough bombs to do this.
• There are no bombs of high enough yield to do this.
• Bombs of high enough yield to do this would have to be buried deep in the earth's mantle to do this; otherwise they would simply blow away the atmosphere leaving the earth itself "untouched".
• No country fighting a nuclear war would spend the effort and money to bury gigantic nuclear bombs deep in the earth's mantle, when it would be much easier and cheaper to simply drop lots of low to medium yield (~10 KTon to 500 KTon) bombs from above on their enemy. Drilling into the earth's mantle is not even possible with current drilling technology (Project MOHO in the 1950s to do this was a complete failure and no significant such work has been done since).

Don't worry, you would be dead due to any of dozens of other nuclear weapon effects (from blast all the way to decades long nuclear winter) in an actual nuclear war before the earth itself would be touched. Even in a war that incinerated and radioactively sterilized the entire surface of the earth, the majority of the biological mass on earth (subterranean bacteria) would not even notice the war and in a few thousand years would fully repopulate the surface and evolution would continue as it did from many other massive extinctions.

High yield bombs (~1 MTon and larger) are rare these days as their military effectiveness per Ton of yield is much lower than that of lower yield bombs. The major reason in the 1950s and 1960s for very high yield bombs was targeting inaccuracy. Modern delivery systems have much better targeting accuracy.