Must be hooked directly to the TV is both cases. There are no external video inputs on any Version STB. Specifics depend on what inputs your TV has.
what is the proper way to connect a dvd player / blue ray to tv and verizon fios?
I would say HDMI from your player directly to your TV, Also Ethernet hardwired to a lan port on the router as the prefered method. If a hardwired connection is not possible with Ethernet CAT5, the a MoCA bridge can be used to pick up a network connection from your coax with the use of a bi-directional splitter. Last resort a wireless bridge or adapter.