Breeding crickets is fairly easy. Just put a dish that is about six inches across and a couple inches deep in with your crickets. Fill it with moist dirt and the crickets will waste no time laying eggs in the dirt. This is if they are adults of course. When the have wings they are adults. The females are larger with a long pointy thing coming from the end of their abdomens. Leave the dish in with them for a few days and then remove it. I put mine under a 50 watt red heat bulb and they hatch in about a week. Make sure to mist the dirt everyday to keep it moist.
Never had a mite problem with crickets. I get mites in the mantid cages though. You don't have to use a heat source for the eggs it will just take them longer to hatch. In a warm area will do fine. Just keep it moist though. Wood shavings I am not sure about. You could use about anything really though I guess.
They are probably grain mites, you will see them crop up when you have some kind of moisture souce in the cage for long periods of time, several days.. especially if you are feeding any kind of grain.