Running PS3 through PC for GTA V

Not possible. You might be able to hook up the speakers to the PS3 but you can't go through your PC

No, but you can install neurointerface into your cerebellum and run it directly into your brain.

why cant you just hook up the speakers to the tv your ps3 is using...?

If your PC supports HDMI input, you could use that.
However, let me warn you that it's tedious work and it has a chance of failure.

I could just plug my ps3 into my subwoofer last time I tried this, then change the sound to be speakers and not hdmi (monitor speakers).

HDMI -> Monitor -> PS3 Video
Sound cable from PS3 -> subwoofer -> PS3 sound
Setup in ps3 options.
I forgot what "sound cable" is but last time I did this it was something I had on hand.

You can do this with a switch. I had a setup with my PC, X360, Original Xbox, and cable box all running through a switch via component cables to use my monitor and sound system.