>1. I was thinking of replacing the hive's solid bottom floor with the type of screen used in SBBs to assist in house keeping, mite drop, etc. My only concern the winter. Do you suppose that this could pose a chill problem for the bees?
If you leave it open. Yes. If you have a plastic cardboard tray to slide in, no.
>2. How can I go about splitting a Langstroth hive into a TBH? I am thinking I could put a caged queen into the TBH and shaking bees from the host hive into the TBH and let it build up as if it were a package start up.
If you build some "swarm ketching" frames (see www.beesource.com
plans) or just build some frames to fit and tie some brood comb in the frames (a cutout) or you just build the Top Bar hive to take Langstroth sized frames and then mix them with top bars, you can get some brood in it.