Part 2 - What sort of ceiling fan support do I need where I can't find framing?
The box you used is for a light fixture and is designed to be installed during construction before the drywall is installed. It is not designed for a fan, and even for a light it cannot be installed with the ceiling drywall already in place. 

You need to get one that is listed as retrofit for a fan, e.g., Home Depot ceiling fan retrofit The retrofit ceiling fan support allows one to expand the support against the ceiling joists by rotating the bar, then the box is fastened to the bar. See the video on the link.