Black Jake

Would that happen in headphones though? Each ear is still getting it's own signal, and given the speaker wires inside the headphone should just be two wires I don't know what else it could be. I've never tried listening with just one earphone out of phase.
 
If it is a phase issue, (and it could still be your brain playing tricks) then yes, it's normal. If you cut out one signal side you won't have the phase cancellation. The simplest way to explain it is that sound is in waves, like a sine wave. Typically, they're in sync, like the left side, and the output adds together. Say the height is +1 and the valley is -1. Add the two together. Normally it's 1+1, so you get 2.
When the phase of one is inverted, like on the right, then it still adds those, but now it's -1 +1, so it cancels out to zero. This is what noise cancelling headphones do.

If you just take the left or right individually, then there's no phase cancellation happening since it's not adding the opposing channels together.
I think if it was bridged it would've killed the speaker. He should be able to swap the wires on either earcup.

Phase cancellation is when the waveform of the audio is cancelled out by the opposite audio waveform, so, if your left and right sides are both playing the same audio (vocal tracks are almost always panned center in audio) and the phase is inverted on one side (creating the opposite waveform) the vocals from each side cancel one another out. If you pan further to one side or the other the two sides no longer have identical waveforms as one is louder than the other, because of this the vocal is no longer perfectly cancelled and it comes back.
Hope that helped.

If you aren't getting lyrics I would think it's supposed to be a "surround" headset but it's not working properly. Though the left and right should still have lyrics. Having it detected as "speakers" isn't a problem. My Realtek driver defaults to calling the rear 3.5 speakers. You can rename it if you want. If you click on configure you should set it to stereo and when you test them it should play out of each ear individually.
 
I can't tell what kind of input jack it has, is it a 3.5

Ethernet is designed to work up to 100 meters. No matter if the cable is 1 meter long or 100 meters, the performance would be exactly the same (* see fineprint). You'll get super low latency since the signals are traveling at super high speed ( ~ 299,792,458 meters per second) and very high reliability, while through wireless the data has to be arranged in packets, sent through the air and be reflected by walls and shit, arrive at the other end and converted back into ethernet packets or data may have to be re-transmitted in case of errors.
 
* fineprint : depending on the quality of the network cable you use, some network cards may have problems with very long cable lengths IF energy savings options are enabled in the network card driver... see "green ethernet" or "low power" modes in the network card's driver configuration. By default, most network cards enable these "green" features which are supposed to lower the transmission power of the network cards or adjust the power dynamically in order to save maybe a third or half a watt of electricity.
 
Some kinds of cheap ethernet cables are made out of copper clad aluminum (CCA, aluminum wires coated with a very thin layer of copper) instead of pure copper because these makes such cables cheaper (copper is more expensive than aluminum). The aluminum in the wires increases the resistance of the wires and this means if you have two cables of same length, you need more power to transmit data through the aluminum based cable in order to get the same signal quality on the other ends. 
For 5-15 meters of cable, the composition of the wires doesn't matter, but at 60+ meters, it does matter.
 
 

An ethernet cable will be faster.
Even standard cat5e handles at least 1gig at 100m
if you can, wire up as many devices as you can

Assuming ideal conditions, neither or is better since the internet is likely going to be the bottleneck. However, Wi-Fi is less reliable and the bars don't really mean anything other than the signal itself. If you have a lot of other Wi-Fi networks on the same frequency and channel, even if you have full bars, you can run into connection issues.
 
If you go the wired route, the length of the cable largely doesn't matter. For instance, Cat5 is good for 100m before you'll start needing repeaters to ensure reliability.

Ethernet cables are always better, faster, more reliable, etc.

cable would be a more stable connection

the best solution would be a 70m coax cable and just put the router by your pc.

coax can go farther than ethernet , it already went from the street into your house with nothing in between a little more won't hurt it.