You are talking about sarcasm. Not irony. And a commonly made grammar mistake isn't irony. Unless your whole post was wrapped in a big <sarcasm> tag and I've just made a fool out of myself.
The relationship between sarcasm and irony is subtle; sarcasm often makes use of irony, but is characterized by its "biting" nature. The quote from my daughter is ironic and sarcastic; the quote about "caring less" is ironic, and may or may not be sarcastic depending on the context.
Irony here refers to verbal irony, a discrepancy between the literally meaning of a phrase and its intended meaning, such as saying "What a nice day!" when it is raining.
Thus, "I could give a shit" and "I couldn't give a shit" are identical in meaning, as the former is doubtless intended ironically. Similarly for caring less.
No. He is talking about irony, not sarcasm. Irony is typically understood to mean saying A while being aware (or of the opinion) that !A. Viz. "Nice hat, dad", or "Real good idea" (when it's not). Sarcasm (cutting remarks) often involve irony, but not always; it's an orthogonal concept.
Also, dropping the "not" in "Could not care less" is not reasonably said to be a grammar mistake. It's usually not sarcasm, either. Whether you agree that it's irony is a different matter (I'm pretty sure it's not).
