No, it shouldn’t matter where you power the digital box. It shouldn’t hurt to power it from a conditioned source, but it shouldn’t make much of a difference to the digital box and as a matter of principle I’d like to keep all of my digital as far as possible from the analog.
The optical interconnect is POF, it’s connectorless, here’s a video showing an installation :
There’s a little discussion of it in the following post and below: