Installing a projector a ceiling junction box
Your cord penetration needs to either be grommeted, or use a proper cable clamp in a standard knockout hole. They sell junction box covers with standard knockout holes. 

Mechanically, what you did is fine as long as the projector weighs less than 4 pounds.  If it weighs more, you need to properly tie into the fan support structure in the way that you might for a chandelier. 

The data cable cannot run in the same in-wall conduit or raceway as the power cables.  You might consider stick-on surface mount wire loom for the low-voltage cables.  Alternately, you could remove all mains voltage wires from the conduit, and replace them with signal cables and 12/18/24VDC to power the projector, e.g. Extend the wires on the projector's wall wart.