I think the territory just has to have your units in it, period. Otherwise they would have explicitly said “territory you control.”
So, by extension, you wouldn’t be able to use the Card on a territory that you own, but is occupied by your ally’s units + Zombies.
Ex. I’m playing as USSR and have the card. Karelia has 2 B INF and 2 Zombies, so is technically “owned” by me.
In this case, I can’t use the “Zombie Mind Control Ray” on Karelia unless I can NCM a Russian Unit into Karelia first.
Re Your Second Question: An IC is technically a unit. FWIW, from an in-game perspective the explanation for why the Zombies need to exceed the IPC value of a territory with an IC is that “the factory workers put up resistance”.
Thus, I don’t see any reason that the factory workers can’t use the technology they developed to mind control the zombies.