Playing with the microphone is the one that does my head in! Your sound man will hopefully have set it up just right for you, so leave it alone unless it develops "microphone droop" or you're in a quick change situation after someone much taller/shorter than you has just used it! Do NOT massage it, keep taking it in and out of its holder, just LEAVE IT ALONE, and twiddle your thumbs instead!
And as an aside to that, try to stay 'on mike" while singing: glancing down at your fret-board (or in my case, buttons) can take you right "off mike", so know your instrument well, so that you can do the playing part by "muscle memory".
And hands: do not wave them about, unless its an action song or emphasising a point, conduct yourself (this seems popular among younger singers these days, why?) Arms loosely by the sides is fine if you're not playing an instrument: least distracting.