OK so DAC stands for Digital-to-Analog Converter, now a USB DAC would take all the audio conversion out of the PC where electronic interference happens or whatever they call it theses days, then you can run that straight to the speakers. Bear in mind this is only worth it for high end speakers.
I wouldn't bother recording with another computer, but if you're intent on it, you would most likely have to run two output sources from your pc, having them duplicated with the same thing on each, or a splitter, then you'd need some kind of capture card, either an external one or a pci-e one if it's another desktop. Then you would run one signal to your screen, and the other to the input of the capture card. i think that if you went into the capture card and then out of the output you would get to much latency to play games.
ShadowPlay from nvidia has basically no framerate hit and is free, and works with most modern GPU's, so just use that, or the AMD equiv.
So networking, best case scenario, you want an ethernet cable running directly from your router/modem, if you have a modem and then an aftermarket router, try and take it directly from the modem for the best connection, but most modems only allow one port to work when in modem mode, so what I do is I run my VM SuperHub 2 with the radios (2.4 and 5GHz) turned off so that I have use of all ports, but then I have my airport extreme as the main router, plus I go into that as I dont stream and I backup to my airport, so it gives me fastest speeds. A good mobo should have a good ethernet port, but if it's maybe a cheaper one, investing in a Gigabit card and possibly a gigabit switch may be worthwhile, if you can get those speeds. I get 200Mbps, and I think that's fibre, so idk what you get.