When is a good time to transplant my butterfly bushes?
You can transplant prior to new growth in spring; otherwise, wait for fall. This article will help: https://www.gardeningknowhow.com/ornamental/shrubs/butterfly-bush/tips-for-transplanting-a-butterfly-bush.htm
My plumbago bushes freeze every time we have a freeze, and they are on a slope facing the house...now all brown. I wonder if I was to plant Buddleia, would it be better at resisting freeze?
It will likely not fare any better. I would recommend covering the plants whenever a heavy frost or freeze is imminent. Here is more information: https://www.gardeningknowhow.com/plant-problems/environmental/tips-for-saving-cold-damaged-plants.htm, https://www.gardeningknowhow.com/plant-problems/environmental/frost-how-to-protect-your-plants.htm, https://www.gardeningknowhow.com/plant-problems/environmental/protect-plants-in-freeze.htm
When should I trim dead flowers from ends of bushes? Or, should I just leave them alone?
This article should help: https://www.gardeningknowhow.com/ornamental/shrubs/butterfly-bush/butterfly-bush-pruning-how-to-prune-a-butterfly-bush.htm
Butterfly bush brittle when I was pruning. Is that the way it should be? Should it be a little pliable?
This article should help determine if the bush is still alive: https://www.gardeningknowhow.com/plant-problems/environmental/how-to-tell-if-a-plant-is-dead-and-how-to-recover-an-almost-dead-plant.htm
Inspecting the butterfly bushes after this winter, the bark on the branches that are coming out of the ground are all loose - like they will fall off and leave the branches "bare." There was mulch around the roots over the winter. Will this harm the bush? Can insects hurt the bush? Are we losing our bushes? What can we do to protect the bushes? I did prune the bushes in the fall after they had bloomed.
This article has some general information on butterfly bushes. https://www.gardeningknowhow.com/ornamental/shrubs/butterfly-bush/butterfly-bush-pruning-how-to-prune-a-butterfly-bush.htm
Also, this article will tell you a bit more about peeling bark: https://www.gardeningknowhow.com/ornamental/trees/tgen/peeling-bark-on-trees.htm
Finally, assuming that you have a Buddleia (there are several plants that go by the common name of butterfly bush,) that peeling bark is natural as the plant grows older.
I have a butterfly bush that has gotten larger than I want it. Can I cut it back and, if so, when and how?
This article will help with that: https://www.gardeningknowhow.com/ornamental/shrubs/butterfly-bush/butterfly-bush-pruning-how-to-prune-a-butterfly-bush.htm
The winter was severe. They do not have any leaves yet and it's 04/26/14.
Butterfly bush (Buddleia davidii) is a very large group with many cultivars, all of which are not reliably hardy in zone 6. You do not mention how long you have had this plant, but it's possible that the winter was severe enough to damage it, and you might still see new growth coming up from the roots. On the other hand, it may have died. There are plenty of other varieties you can try. This article has some more information: https://www.ipm.iastate.edu/ipm/hortnews/2002/2-22-2002/butterflybushes.html