A "mixer" is basically the sound card in the computer for your purposes. It "mixes" the sound volumes together for all the different noises and sounds the computer can make for whatever programs are running. At some point if you have 3 or 4 apps running that all have sound output and you click on the speaker at the lower right of your task bar it will give you a separate volume control for each of those apps, plus the main volume control. That's what a mixer does.
Your comment about answering the call with a button on the headset, assuming it's a USB headset, is valid, but the software application you are using has to be aware that button is there, and it has to be programmed to know what to do with it if you press it. Most of the time on Microsoft Lync and some other products they will work with those buttons - I don't think AC-Win is that advanced, especially V2, and I just installed V4 - I don't think that can do it either. I also have the Openscape Personal Desktop Client that lets me log into my phone from my PC - I believe that is the groundwork for how AC-Win is built. That will allow the use of the volume buttons, and the mute button on my headset (Plantronics USB Blackwire) but doesn't acknowledge the hookswitch button for that particular application.
You will probably need to have one of the higher gurus on here that are connected more closely to Unify find out the answer to that for you. I would be most interested if the answer is Yes. I know with the right connection cable I can use a wireless headset on my Openstage phones, but not the console as far as I know.