"Ok, here's another question for you, Apis or Badger or whoever can help me out! I have already seen a mite. There was also a moth in the package. I did not think to get it out before I put the package in the third deep. How do I proceed with preventing this from getting worse? I know I need to get screened bottom boards to start, but what is standard procedure for controlling these pests in a new hive?"
apis63, focus on getting your bees hived and strong.......mites; sometimes package bees come with mites...some worse than others.
once your bees are hived and in warmer weather, you can evaluate what the mite population is, and treat as needed later, but not right now..........a moth in the package?
when your bees have been hived, when weather/temps are conducive to opening the hived package, i would say next weekend, after the temp warmup, take a look in there and see what's going on. i also think the bees will take care of the moth, but to be proactive, check all your frames.
screened bottom boards are not a 'fix' for any pest, and IMHO, you don't need them...........