First of all, thank you for your patient explanation. As for whether Gil is a virgin, I don't think he is. In Lars Episode, the CG shows how close Lars and Gil are, which makes it hard to believe that he is still a virgin. Gil said he was a virgin, maybe just joking.
I don't understand why Parker should do these things, even if Gil asked him to do so. How Lars and Gil get along, It's none of Parker's business.