So Rand's ta'verin influence, how far does it extend? Clearly, Perrin had to leave but to what extent he said he could resist but Matt said he could not to what extent, can ta'verin resist another?

I think it also has to do what the pattern had in store for you, Perin's destiny was in the Two Rivers so he had to be able to resist.  Where Mat was destined to go with Rand to the waste. Had Mat broken free and went to the Two Rivers he would of died.  You saw later Mat really never felt a OMG Rand needs me pull like Perin did.

some book in the series told that Rand's tavereness could cover an entire city.

 

from my understanding, taveren influence the lives of non-taveren; and the Pattern controls the lives of taveren.

 

Rand’s Taverenness can bring people across the whole world. 

Mat’s power brought him Tuon.

Rand drew Male Channelers to him to join the Ashaman from far and wide before he started the recruiting.

The twisting of chance seems to be a more local effect. No babies dying in a whole city seems to the range of the talent. 

It's fairly incredible like potentially quite heonstly earth/sorta planetwide influence.