A second suggestion is that nuclear decay in surrounding rock affects the Carbon-13 or Nitrogen-14 in the diamond to create recent Carbon-14. This could happen, but calculated rates of formation of Carbon-14 would be thousands of times less than the measured amounts.
They would, if one assumed the world was only a few thousand years old. You can't find rates, for formation of such things, unless you have some idea of how old it is. Here, he's just assuming what he intended to prove. If the deposits were very ancient, it would show just what it shows.
The third suggestion is that radioactive atoms present in the diamonds' decay could occasionally emit a Carbon-14 nucleus rather than an alpha particle (which is a Helium nucleus). The rate of decay of carbon nuclei. however, would be hundreds of thousands of times less than what is needed to explain the presence of Carbon-14.
Maybe. But simple conversion of nitrogen to carbon-14 over hundreds of millions of years is, by itself, able to explain what we see.
Thus, DeYoung notes that the presence of Carbon-14 is good evidence for a young earth.
Only if you assume a young Earth in the first place. He's just chasing his tail. Bottom line, we know C-14 is being produced from nitrogen in buried diamonds, because nitrogen exposed to radiation, produces C-14. (and as you see, the matrix in which diamonds form has radioactive elements)
The argument you've presented is:
"It couldn't have been very long, since we know they've only been there a few thousand years, and there wouldn't be much forming in so short a time."
Why not just accept what the evidence indicates?