Can you use a Cache token to reduce the cost of a purchase to zero and below? Or is there always a minimum cost of 1, a limit that cannot be lowered below?
To zero, sure. This is a good way for a faction to mitigate low-material output of worlds. It can't go negative because no unit costs less than 2, you can only use one cache per unit, and you can't use them for order/combat upgrades.