Not every NPC is designed to respond to greetings, unfortunately. This may mean they either don't have a quest for you, or their quest might be a bit more complicated. You probably don't have to worry about it for now.
That's true, we actually had a recent bug where NPCs were not responding to greetings or other form of player interactions.
As for relationships, that's not really possible, but you -can- have relationships with certain promiscuous gods, like @Haern. Good luck with your divine trysts!
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