A couple weeks ago I split one of my hives and went in today to check on their progress with making a new queen. I found a an empty queen cell no queen and no sign of a queen. I wasn't expecting to find a queen just hoping to find a capped queen cell. So I took another frame from my other hive with brood eggs and larvae and what I think to be a swarm cell and put that in the split. Did I do that right was that wrong? Also the split has some signs of wax moths and there are mites on a bunch of the bees. How do I treat this I haven't had mites before and don't know what to do about that.