This is not divorce petition but it is a petition seeking to annul your marriage.
If there are no proper grounds for annulment, the court may even dismiss the petition even though you are not appearing and allowing the case to become exparte.
Better participate in the proceedings and contest the case properly on merits and see if you can challenge her grounds.
Yes you can appear before court on the date of hearing and seek time for filing counter.
Who knows what she has in her mind, such things cannot be predicted.
The legal fact is that she can remain or live in your house till the time she remains your legally wedded wife.
There is no procedure to file a counter.
You may have to prepare a counter denying all her allegations and submit it before the court.
You may take the assistance of a lawyer to prepare the counter and you can submit it as party in person also.