4H is a member of the Illinois Panhellenic Council. They have a house. I don't think they participate in the later rounds of formal recruitment, though. I think they have two "interview weekends" per year where they meet PNMs and do membership selection.
Correct, on all counts. They are a full voting member of the CPH, which is obviously a privilege that is almost unheard of for groups not in the NPC, on any campus. PNM's visit the house as a sort of informational visit in the first round, but their membership selection takes place when women are still high school seniors.