I used OBS Studio to stream. And still do. If you don't use wk3d9wnd module, you'll have to stream WA via display capture option.
If you have wkd3d9wnd module enabled - then you'll be able to stream via game/window capture.
Which will allow you to minimize and do other stuff, while viewers will be seeing game you play.
I advise you to go with 2nd option.
For voice chat, I don't know what mumble is, but discord is pretty popular gaming platform nowadays, everyone i know use that. So if you want, join us there and invite your buddies to join you in voice while streaming. Link is here under my post, just click the thumbnail.
Or other solution: just make your own server and invite ppl there if you want to have guaranteed privacy.