1. There is a procedure for serving notice. You are supposed to serve her the notice at her present address. If her present address is not known then you are supposed to serve the notice to her last known address. If she still does not get the notice, you shall have to publish the notice in two newspapers, one in English and another in Vernacular, so that all possible efforts serve her the said notice is taken. Under no circumstances, the duty to trace the opposite side at any cost falls on the complainant,
2. Ex-Parte divorce can not be a common practice. Ex-Parte order is passed when the other side fails/neglects or refuses to attend te Court hearing. In the instant case, it is accepted that the opposite side has been notified by following the laid down procedure and after being notified about the case, she has failed/neglected or refused to attend the case. For the said non attendance after being notified, Ex-Parte hearing will be conducted or ex-parte order will be passed. It is not an approach. It is the procedure of serving notice,
3. Once decree of divorce is issued, she can file an appleal before the appellate Court challenging the decree of the Court lower within the limitation period being 3 months. After that her appeal will be time bared. She cannot challenge the said decree issued by Indian court before US Court,
4. No. For filing divorce suit, you shall have to be personally present in India and after the case is filed, your POA holder can follow up the case for you.