What is the stance court is likely to take in this situation? When would the court consider the summons as "served"? What happens if the summons are not served, for whatever reason?
If she expresses before court that your address in India was the last known address, she may seek permission of court to take steps to serve summons by substituted service of summons i.e., by publishing the same through newspaper, then that will be deemed as proper service of summons.
2. Let's say the summons get served. Can H submit response in writing or via a lawyer? Or is H required to appear in person in front of the court on the date indicated on the summons?
On receipt of summons the H has to appear before court either in person or through his lawyer.
However in family courts' the presence of both parties to dispute is mandatory or they can be represented through their power agents too.
3. Does W also need to appear in court on the date on which H is supposed to appear in court? If W needs to appear too, is that true for every single hearing?
Both the parties are to appear before court, see the above anser for further details.
4. If H decides to respond making the counter-accusation that W's behavior was cruel and constructive desertion, would H need to file a separate petition, or could this be included in H's response to W's petition? If H needs to file a separate petition, would H need to appear in court physically, or can this be done via a lawyer?
The H has to appear before court whether he files counter or not, even if he engages an advocate.
H can file his counter to her allegations denying them in the same case itself.