couple of questions
when the circuit is 'open', it means that there is air separating two ends of the wire. But it is possible to run a current across the air (for example, think of lightning, well technically it might turn the air into plasma first) But the point is that there is no such thing as a truly closed circuit, because we can think of the air as 'closing' the circuit, but since the resistance of air is so great, we can for all practical purposes say that that the circuit is 'open'.
the rule about parallel voltage... there are several ways to 'reason it'. One way is to think about the potential at each point in the circuit. the change in potential around any closed loop must be zero (otherwise, it wouldn't make sense, because we assign the potential to have a particular value at each point in space, so it cannot be defined to have two different values at the same point!)