Its great that you want to start an AAR with Armenia, but I dont know what you mean by "Persian" even though there defenitly are cultural and administrative similarites, Armenians are an entirely diffrent ethnic group with a diffrent language, and culture.
now to answer your questions:
Hai means Armenian Hayasdan means Armenia. Hai comes from Haik the semi-legendary Patriarch of Armenians. The story goes that he and his highland tribesmen were freedom loving people, and that Bel the king of Babylon was trying to rule over them. Haik was a gifted archer, and he slew Bel in battle. Armenia is derived from the Armina or Armen tribe which gave the people and the region the name that all non Armenians refer to.
Haikakan means Armenian. It means in Armenian in the sense of something being armenian. For example Armenian dance- Haikakan bar. Armenian wine-Haikakan gini
The issue with the spy and diplomat, It could be a possibility that they are related to the Yervanduni, also it could mean that they serve them. So either or is fine.
So to wrap it up. Armenia- Hayasdan Armenian/Armenians- Hai/Haier Armenian (as in something being Armenian such as Armenian dance, or Armenian wine) -Haikakan
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