I'm about to go to pre-cana. If the priest finds out I'm not a virgin then can the church deny my marriage application? Does the priest have the liberty to ask? Do I have the liberty not to answer the question in order to continue the pre-cana?
Go make a sacramental confession with a Priest other than the one conducting your Pre-Cana, and after the confession ask him. But I don't believe that the Priest is allowed to ask, but I don't believe the Church would withhold the Sacrament. Lack of virginity is not a reason for withholding the sacrament, for one can marry after the first spouse has died, and they would obviously not be a virgin.
Q. [Pre-cana priest] Are you a Virgin?
A. [First appropriate response] May I ask why? [establishing relevancy vs. morbid curiosity]
Relevancy: In the case of pre-marital sex being the reason for the lose of virginity.
Reading the question, I was thinking under what circumstances pre-marital sex might come up and it is in, for example, the following two elements in Marriage Preparation Policies:
Say pre-marital sex is present at the time of marriage but the sex is with someone else other than with the party marriage is being contracted with. That could be adultery at the time of marriage and if proven later by the innocent party when marriage later breaks, that would be a valid issue for annulment.
The probing into pre-marital sex and the underlying reasons, may also help guide parties to the proper understanding of marriage as the Church understands it.
Concluding, honest responses on all elements of the marriage preparation policy are to be made to the priest conducting pre-cana.