and... (i cut it in 2 posts) About the topic itself 'cable will improve ?'
nobody can ensure it without knowing your real connection up speed.
Your maximum speed is the
minimum speed between these 3 links : 'pc to modem' , 'modem to internet' , 'internet to Site' (with everybody connected)
In rare cases, wifi can be slowed down by local obstacles (room walls ie...)
But in general, Wifi can be easily faster than your connection from modem to net, especially if you try to broadcast connected through adsl or some basic fiber connections.
In this case the limitation is given by the modem (your isp) and wiring a cable will only add a cable attached to your machine (a new trap in your room^^).
So, if you have a way to measure it (your modem's administration page can show you it's own actual limitations) we can answer, else you can just try.
"That doesn't eat bread" (we say it french... it means that it's not a big job to do, not risky and very easy)
Just compare both setups *with cable* and *with wifi* Results can be very different from one room to the other.
to test modem to internet : your modem administration page (ask you isp's hotline)
to test PC to internet (trough modem) :
https://www.speedtest.net/
to test the whole link PC to chaturbate trough modem and internet :
http://chaturbate.speedtestcustom.com/
then yes OBS uses less bandwith than Flash site's streamer and manages the sound much better.
This last point has no comparison, you wil have sound instead of weird ambiance.
Maybe I can add also that you can check the final result by browsing your own page as a viewer.
Just open another browser (ie if you broadcast with chrome, open ieExplore, opera or firefox) and don't connect your profile to browse as anonymous or use another 'grey' profile to check with a password without bothering your followers.
Go to your room and see how it looks like.
That will not use much "up bandwith" but more "down bandwith". It mean that doing this, you'll see a result very proach to what your users have, in real time.
(But forget the idea to test any sound like that ! or only to check music, using headphones)