Can't help with the screen sharing and group chat (both have been iffy for ages for me, and that is before we consider the Linux version).
What I will say though is in the skype options is the option to choose what audio hardware you use, somewhat aside from the mic options in volume manager and whatever else. Several times across many versions I have had microphones or audio output be something different to what the machine is using (and not just HDMI vs 3.5mm sound card ports).
Equally what about a completely clean install of skype. Uninstall it with revo (
http://www.revouninstaller.com/revo_uninstaller_free_download.html , also available on
https://ninite.com/ if you prefer such things) and then install it. Skype has all sorts of legacy settings and configs that the standard uninstall might not get rid off.
One day I might have to look seriously into this discord lark. I mainly write it off as the latest chat fad program (there have been many and this is another proprietary one without the option to hand roll your own server) the kids are using but it has now stuck around a tiny bit longer than some of the others before it.