Translation:Bir asır yüz yıldır.
I would say not in this case. It is really needed for clarity's sake.
It seems in "asır" and "yıldır", the final "r" is pronounced much closer to a "zh." Why is that, and are there rules as to when to say it like that?
Final r's in Turkish get devoiced, especially at the end of phrases and sentences. If you weren't to do this though, everyone would understand you. Many Turks aren't even aware they they do this themselves :)
Ahh, okay, that makes sense. Does it have to do with the fact that Turkish r is a flap, and that's similar to a stop?
There are none :) In some set phrases you can just use one (i.e. Yeni yıl, not Yeni sene)