Communication between microcontroller and separately powered PCB
A single wire may or may not work - check to see if your boards have a common-enough ground.  You may get lucky and it will be just fine (since both boards will be connected to the mains ground, at least in some way).  At the very least, you can probably run two wires - one to tie the two grounds together and another for the data.   If for some reason you can't have a common ground, you can look into optoisolators.