b) Do I get charged by my ISP on a per-device basis?
Heh, if they want to micromanage...
This is no science fiction. Some big providers in some countries limit the number of device that can connect to internet. You have to register the MAC address of your single PC (which, by the way, is expected to run Windows or MacOS)
In that case, a NAT router sending the MAC address expected by the provider could have (maybe, possibly...) been very handy. (I won't tell more, even though I have left the country and the provider in question)