One question at a time.
I will simply say this. The Passport Canada office confirms that in order to receive a diplomatic passport a traveller must be a government official on official government business or married to or the common-law spouse of such a traveller.
On the issue of invitations, I am married but I do not know what invitations she gets from the government. Any invitations with which I am familiar have been for me and a guest if I wish to bring a guest. That is my experience on how these things tend to occur.