The way to go is a cheap HDMI Splitter, if you find the right one. Another, much easier and cheaper method, is the use of a HDMI splitter. A splitter

A USB to coax converter is a DDC, ie, digital to digital converter, for converting a USB audio signal into 75ohm coaxial SPDIF. Unless what you have is a DAC-HPamp

Input lag is caused by high latency. Moving to Display will only increase your band with not decrease the latency between the input to display. Does DisplayPort affect performance? No.