I use sheepskin mitts so I can't really say I'm an expert on when to replace a MF one, but I usually replace my wash mitts when I notice it starting to shed from overuse or if it becomes extremely dirty/stained. Sometime this will mean 1-2 washes on really beat up cars coming in for an initial service, other times it can last me 20 washes on light, weekly maintenance washes.
I do the same thing with my mitts as I do with towels, in that it gets downgraded from paint, to wheels, to exhausts, etc. before it goes in the trash.
As for actually washing it, you should wash it thoroughly after every use because you don't want the soap settling/hardening inside of it. I thoroughly wash and inspect each mitt I have used after each detail job, then categorize them accordingly. Hope that helps.