Learn Turkish: Abartmıyorum, hayatımda bu kadar kibirli bir adam görmedim! - I am not exaggerating, I have not seen such an arrogant man in my life!

Yes! You could replace the comma and say Abartmıyorum, üstelik hayatımda bu kadar kibirli bir adam görmedim! (I am not exaggerating, moreover I have never seen such an arrogant man in my life!). Both üstelik and ayrıca work perfectly here to add emphasis and smoothly introduce your second, stronger statement.

Why does the English say "I have not seen", but the Turkish uses the simple past tense görmedim?

Turkish doesn't have an exact equivalent to the English present perfect tense ("have done"). When talking about life experiences up to the present moment, Turkish naturally uses the definite past tense -di. So, depending on the context, görmedim covers both "I didn't see" and "I haven't seen."

Could I use böyle instead of bu kadar here to mean "such"?

Yes, you can. ...böyle kibirli bir adam görmedim is also entirely natural and means almost exactly the same thing. However, bu kadar literally means "this much" or "up to this amount." Using it emphasizes the extreme degree of the man's arrogance, making the complaint sound a bit more intense.

The verb is abartmak (to exaggerate). Why doesn't the 't' change to a 'd' when adding the -ıyorum suffix?