Is 1 indicative of current flowing? Or not flowing? Is that consistent with a given chip, let alone an entire system? Is it always DC current, or can it be AC? In fact, is the 1 represented by current, voltage, and/or frequency?

There's lots of different answers here in different contexts. The reason 1s and 0s are good is because they represent the information in the digital domain, not the implementation in the analogue.