First of all "kusura bakma" is for 2nd person singular (sen), so it's not in the polite form (siz), which is: Kusura bakmayın.
I can say that "afedersin/afedersiniz" is exactly the same as "özür dilerim" or "pardon", the latter, I'd say, lacks the spirit... Anyway, you can use these interchangeably.
Kusura bakma, however, has something warmer in it. It sounds much more sincere. For example, you are at your friend's house, you dropped the glass and it got broken, you would say: Kusura bakma, or Kusuruma bakma lit. please neglect my fault. Or perhaps, you met a friend of yours after a long time, he used to be married but not anymore, however you don't know that. You might say: "So, are you two still dreaming about having twins?". He would tell you that he got divorced, to which you could say: "Aah! Kusura bakma ya...".
Of course, in all these situations "özür dilerim" or "afedersin(iz)" would also work, but they are "colder" than "Kusura bakma(yın)".
"Afedersiniz" exactly means "excuse me" , when you want to ask a question or request something you can say this word.
"özür dilerim" has the same meaning with " I am sorry" , I mean when you do something wrong you can say this phrase
and "kusura bakma" is generally said to the people whom we are more closed. For example one of our friends say:
- I waited you for 2 hours yestarday why didn't you come?
and our reply can begin with:
- kusura bakma I totally forgot it.
Actually it is nearly same as özür dilerim, but we prefer to say it to our friends and it is more informal.
Özür dilemek is a misconstruction but nevertheless standard (and correct) form. The original forms were özür beyan etmek "to declare/give/offer/provide an excuse" and özrün kabulünü dilemek "to wish the acceptance of the excuse." The latter was reduced to özür dilemek (in my opinion, influenced by another expression af dilemek "to beg pardon" and özür gained the sense of apology. Özür and mazeret are from the same Arabic root (عذر).
An obsolete expression from the same root was i'tizar "to give/offer an excuse".