Thanks, Ben and 15th. Just as "getting old ain't for sissies", neither is beekeeping. I've only been at it for a couple of weeks, but I've been learning so many things... usually the day after I really needed to know!
15th, your comments helped me avoid what might have been a big mistake -- taking brood from my friend's hive. Now that I think about it, her colonies have some problems of their own, and sharing frames right now could easily set us both back.
I plan to do monthly sugar rolls to check for mites, starting in a couple weeks. I've been checking the mite board under the hive in the meantime. So far, no beetles or mites. The bees can't get to the board, so I dusted it with DE before installing the bees. If anything does fall through, the DE should send them to glory. If a mite problem develops, I definitely will treat with the dreaded chemicals. My goal is to work my way into having resilient bees. The transition will take some time, so in the meantime, I'll take good care of the bees I have.
I did some research on that queen cell I found. Turns out it was a swarm cell, not an emergency supercedure cell. Now I have to figure out how to address that urge to swarm. Being less intrusive will help, I'm sure, but I probably need to do more. I haven't decided what exactly, but part of the solution might involve getting that snazzy, mite resistant queen I've been wanting. Never a dull moment, right? I agree, Ben, this forum is a lifesaver for new beeks!