You have the key phrase to Google right there in the text you quoted

A system described in the 2003 United States Air Force report called Hypervelocity Rod Bundles[10] was that of 20-foot-long (6.1 m), 1-foot-diameter (0.30 m) tungsten rods that are satellite-controlled and have global strike capability, with impact speeds of Mach 10.[11][12][13]

The bomb would naturally contain large kinetic energy because it moves at orbital velocities, around 8 kilometres per second (26,000 ft/s; Mach 24) in orbit and 3 kilometres per second (9,800 ft/s; Mach 8.8) at impact. As the rod reenters Earth's atmosphere, it would lose most of its velocity, but the remaining energy would cause considerable damage. Some systems are quoted as having the yield of a small tactical nuclear bomb.[13] These designs are envisioned as a bunker buster.[12][14] As the name suggests, the 'bunker buster' is powerful enough to destroy a nuclear bunker.

https://en.wikipedia.org/wiki/Kinetic_bombardment?useskin=ve...

I don't know.

Shape can change it to be arbitrarily bad; 14 tonnes of 5-micron-thick Eglin steel foil spread over a ten-block area wouldn't penetrate anything, just gently waft down, although it could give you some paper cuts. I suspect it can't make it much better, except in the sense of increasing sectional density by making the bomb longer and thinner, which we already know the results of.

Velocity doesn't enter into Newton's impact depth approximation at all. It does affect things in real life, but you can see from meteor craters that it, too, has its limits.

Target characteristics, no idea, but in a fast enough impact, everything acts like a gas. It's only at near-subsonic time scales that condensed-matter phenomena like elasticity come into play. Even at longer time scales the impact can melt things. This of course comes into conflict with the design objective of the bomb acting solid, so that it penetrates the soil instead of just mixing into it, and can still detonate when it comes to rest. I feel like buried plates of the same metal would have to be able to deflect it? And there are plenty of other high-strength alloys.

Your calculations appear to be off by a factor of ~1000. Not half a kiloton, but half a ton (~500kg), assuming fall in a vacuum (upper bound on impact energy):

  Python 3.10.12 (main, May 27 2025, 17:12:29) [GCC 11.4.0] on linux
  Type "help", "copyright", "credits" or "license()" for more information.
  MOP_potential_energy = 13607*9.8*15000 # E = m*g*h
  MOP_potential_energy
  2000229000.0
  TNT_specific_energy = 4.184e9/1000 # joule/kg
  TNT_specific_energy
  4184000.0
  MOP_potential_energy/TNT_specific_energy
  478.0662045889101

Yet setting off half a tonne of TNT on the ground, or even just under it, won't penetrate 60 meters deep, or even 15; it will just blast open a shallow crater. A shaped charge will do only a little better.