*Like, I'm sorry for what I have said (once). I didn't mean it.*... is WRONG **I'm sorry for what I said. I didn't mean it.** Your question is really about the present perfect and the past. You will have to study that. It's too much to write here. **Have you noticed something about Jack. He looks different. Really? I haven't noticed a thing.**

"I have said" does mean that the person has said something in the past, but it doesn't mean they didn't mean it unless they specify that they didn't mean it. Like, if someone says "I have said I don't like lettuce multiple times." This doesn't mean that they didn't mean it. It means they're reminding who they're talking to what they have said in the past. Unless they say "I have said some horrible things about you. I didn't mean it." Something like that. Then they meant whatever they said. "I have noticed" can be both multiple or singular times. It all depends on the context. "I have realized" generally means a culmination of events has lead you to realize something new and you realize it once until you realize something else. So, "I have realized" is generally talking about your present thoughts about something.

it could be once, or it could be multiple times. There is no way to know unless the speaker clarifies it

jenny, It helps to think of the present perfect being used in two principal ways. 1) duration or repetition To express an event that occurs over a period of time (duration) or repeatedly (repetition) the present perfect is almost ALWAYS used. Words like for, since, and always are indicators of this use. The action continues to the present moment. I have lived here for seven years. I have known him since 1977. I have always said that life is what you make of it. I have said the same thing at least 20 times. I have often noticed that the smell of onions brings tears to my eyes. How many times in the past have you realized that you should quit smoking? 2) indefinite time. When expressing events that occured at some indefinite time in the past, but not exactly when they occurred or ended, EITHER the past simple or the present perfect is possible. This will depend on where you live (the past simple is used more in America) the context (the meaning of the verb) and your preference. Sometimes the present perfect is used to express that a past event is important now--or simply to emphasize the fact that the event has actually happened. I've just said it........or.........I just said it. I am sorry for what I've said......or ......I am sorry for what I said. I've realized that I was wrong.....or.....I realized that I was wrong. I've noticed that you fed the cat raw meat......or..... I noticed that you fed the cat raw meat.

Let me quickly answer your questions one by one: 1) No, "I have said [X]" does NOT mean "I have repeatedly said [X]" unless you specifically add "repeatedly", "often", "many times", etc. 2) It definitely does NOT mean "I have said it but I did not mean it/it was not my intention to/I regret it" (unless you specifically add such a restriction). 3) "I have noticed X" is COMPATIBLE WITH the interpretation [I have repeatedly noticed], but does NOT entail it (nor the converse: it does not imply that you noticed something just once, either). Depending on whether "X" names a unique event or a set of events of the same type, "I have noticed X" will be interpreted one way or the other. 4) Definitely not all periphrastic perfect verb forms allow an iterative interpretation, but this has nothing to do with the auxiliary "have". If the verb that follows it is such that it must be interpreted as naming a unique event, the iterative interpretation is automatically blocked (e.g., "My father has died"). The multiple-event interpretation is not available unless the VP following "have" requires it (e.g., "I have seen hundreds of plays", "I have interviewed fifty candidates", "I have repeatedly noticed such a reaction", etc.). 5) Verbs like "notice", "realize" etc. name (unique) instantaneous changes of experiential state ("achievements"), tend to be used in the simple past (rather than the perfect: such states do not last), and go well with adverbs like "suddenly", but not with adverbs of "duration", UNLESS an iterative reading is licensed by other clause constituents (e.g., a plural object, adverbs like "often"). 6). What makes verbs like "live in [place]" compatible with duration adverbials is that they name lasting STATES (not instantaneous events). States like "live in London" are unbounded unless you specify their duration by means of a suitable adverbial (e.g., "for three years", "since I left school", etc.). Good luck! :-)