This must incredibly frustrating, but I don't think it has anything to do with Gmail, Calendar, etc. It sounds as though it's a domain registration problem due to Google acting as a domain reseller for eNom, or something. If anything, the lesson is, "don't use Google as a registrar", though I suppose you could argue that the bad support is an overall issue.

In general, I would avoid any of these reseller situations, since the error could occur in multiple places and both parties would probably assume that it's the other's fault.