Yes, TV power cable is high voltage, the rest is low voltage.
You can run them side by side, it's just not recommended. With HDMI, in my expeience, it is RARELY an issue.
Per NEC, you can't run high voltage and low voltage through the same holes behind drywall, but there is not the same rules if you surface mount. So, it's just bad practice to do so, but sometimes it is just unavoidable. You run the wires together, then see if you have any noise and separate them.