Your understanding of carbon-14 dating is correct. I've no idea where the author of It Couldn't Just Happen got some of his facts from, but they are simply ... what's the word I'm looking for? ... oh yes, "wrong."
As you correctly stated, carbon 14 turns into nitrogen 14, not carbon 12. He's simply not getting his facts straight here, and that is completely unacceptable for any science textbook, no matter what worldview it adopts. I'd ask some serious questions about whether he's qualified to be writing on the subject, and what kind of editorial oversight it's had. Real science textbooks are peer reviewed.
Again, untrue. Scientists don't blindly assume anything. Scientists have some clever ways of figuring out the original composition of a sample; the calibration curves against tree rings that you mentioned are one example of this. They also do a lot of cross-checks between different dating methods to figure out which ones work in which circumstances and to test the assumptions to see whether or not they are valid.
At best misleading; at worst, completely untrue.
There have been a small number of studies in recent years that seem to suggest that some radioactive decay rates can vary slightly with certain environmental factors. However, the findings are controversial, replication of the results has been spotty at best, the necessary conditions are extreme, and in any case, even if the effects are real, they are far, far, far too small to have any significant effect on radiometric dating results.
Current YEC thinking is that nuclear decay rates must have been much faster — by a factor of a billion or more — during the first two days of the Creation Week and during the Flood. This was the subject of a $1.25 million, eight year project called RATE (Radioisotopes and the Age of The Earth) run by the Institute for Creation Research from 1997 to 2005. Unfortunately, their conclusions degenerated into complete absurdity — they admitted that this much radiation in this short a time would have released enough heat to vaporise the earth's crust many times over.
I think it's pretty safe to say that accelerated nuclear decay in general — and certainly on that scale — is complete science fiction.