So if I'm understanding the pattern correctly, affedersin is informal and affedersiniz is formal?
Yes! Or plural :)
fyi, "Pardon!" is accepted as well. Pronounced similar to as it is in French.
When i was there in turkey i only heard people use pardon
Yes, It can be used too.
Is this excuse me for getting attention? Or excuse me like an apology?
It is an apology type of excuse me. Pardon is used to get through. If I remember correctly, afedersin comes from the turkish word meaning forgive, so it means forgive me. I think, I'm no turkish expert.
both of them is possible
I heard it once in a film as an apology
Does this come from "auf wiedersehen" by any chance?
Nope :) It comes from the the Arabic word 'عفو' (meaning "pardon") and the Turkish verb "etmek' (meaning "to do").
Why doesn't this have an ı instead of
Because the last vowel before it is "e" (affedErsin), which is front and unrounded.
It depends on the pronunciation as the pronunciation of the letter (ı) is different from the pronunciation of the letter (i)
I'm unsure if it's just the recorded pronunciation and wanted to clarify: is it more of an "ar" sound or an "er" sound when 'er' is written?
So during my stay in Istanbul people dont use this word and they use pardon
Basically "I do". But it's used a lot together with nouns to turn them into verbs -- e.g. teşekkür ederim "I do thanks/thanking", but a better translation is just "I thank" or "thank you".