Re: Mic cable adapter. Is this the one I need?
If you need to plug an XLR MALE in to a 1/4" FEMALE socket on the mixer, what you need is a FEMALE XLR-to-1/4" MALE transformer. Transformer being the operative word because something happens electronically as it gets stepped-down for the 1/4" part.
They're pretty common, most stores that sell PA stuff will have it. There are two types: one where it's the barrel and on one end is the 1/4" male plug, and the other where you have the transformer barrel, but then a short cable comes out of it and terminates to a 1/4" male plug. I prefer the latter because it alleviates some of the weight being put on the 1/4" female jack on the mixer.