This person apologizes and sounds like they accept their own mistakes, can they really mean it?

Yes, some narcissists will apologize and acknowledge their mistakes to manipulate others. They can learn how to express empathy without actually “feeling” empathy. They know this behavior is accepted and often rewarded. They can use it to confuse you and pull you right back into the relationship. So while they appear to care, someone who is sorry and accepts their mistakes will also change them, so pay close attention to their actions because they usually don’t match their words and within a short time, often immediately, they will reoffend for the same actions they apologized for.