Zero quality beehive resources:
I think its save to say that Zero quality honey and/or wax are not possible. CQ: Beehive resource quality probably actively capped to a minimum of 1.
Did two runs of planting 1q crop-seeds with a beehive that was already giving 1q honey some time ago. Both times resulted in 1q honey. (Stored the used beehive inside a cabin between the two planting sessions, to only target resources given by the planting stage of the crops. Just in case.)