Sounds like you're overheating which is causing the laptop to sleep or shutdown. Download MSI Afterburner and monitor your CPU & GPU temps. You probably need to open up the laptop and blow out any dust that's accumulated.
Yes, assuming you want PC audio OUT to TV audio IN (i.e. hear PC audio through TV speakers).
You need a Y splitter like this:
https://www.amazon.com/Belkin-Audio-Cable-Splitter-1-Mini/dp/B00004Z5CP?ie=UTF8&*Version*=1&*entries*=0