Regarding Ivy, as I understand things even if the Archive didnt innately grant Magic on it's own, Ivy was born to a actively magic-using lineage going back most of Human History, so I think it is all but inevitable that said Bloodline would have developed/mutated Magical capabilities through chronic exposure.
I'm mostly thinking about Ivy's magic use as an exponentially greater example of Victor Sells. He didn't really have all that much power, fueling his stuff with rituals and thunderstorms, but he was able to do enough research to do some reasonably powerful things. If he was as smart as Butters, with a teacher like Bob, I think he might've been able to do quite a lot. With
no magic, Butters was able to mix potions and make mind fog bombs. I don't know if Bob was powering the skateboard, but I doubt he had anything to do with those other two things.