These are the sort of questions that Nick Smith says in "The Penitent and the Penitentiary" he is considering as he writes his second book on the topic of apology. His first, I Was Wrong, identified the elements that give apologies their "core moral meaning". Those apologies that meet these benchmarks may be considered "categorical apologies".
There are 12 benchmarks, including acceptance of blame, identification of each harm caused by the act, awareness of the moral principles that were violated, and intention to advance the victim's well-being in making the apology (as oposed to merely benefit the apologizer).
Now he is working on a new book, Apologies in Law, which explores how apologies should be treated legally.
This is a well-written article with provocative questions and at least one brilliant take-away line: ""I view the words 'I'm sorry' with the same scrutiny as if someone said 'I love you' on the first date: I would need to know much more before I could make a well-informed judgment."