I don't think you can tell the diff between male / female beetles.
I use a 4 bin system, one for eating size worms, one for aliens, one for beetles....and another that eventually will be my first wee baby mealworms. (once eggs hatch will dump beetles bin into baby bin and give the beetles new food/bedding to lay more eggs)
For moisture I use damp sponges on a plastic lid
I just bought a few sponges and cut them up. You can set them on a bit of plastic or aluminum foil too. Plus a carrot or potatoe set beside it.
I use a large metal screening type sifter to remove the frass and dump everything else back in. I use bran and oats in the ready to eat meal worms but bran only in the rest cause it's easier to see whats happening. I put some of Hazels ground kibble mix in with the grown mealies.
I don't plan on sifting frass out of my beetle bin because I would lose all the eggs! Better to wait until babies are hatched and grown a bit.