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Yes, they should be fine. This article will help with transplanting them: https://www.gardeningknowhow.com/ornamental/shrubs/butterfly-bush/tips-for-transplanting-a-butterfly-bush.htm

It has transplant shock. This article will help:
https://www.gardeningknowhow.com/plant-problems/environmental/learn-how-to-avoid-and-repair-transplant-shock-in-plants.htm

They should regrow their leaves. Here is information that may be of some help: https://www.gardeningknowhow.com/plant-problems/environmental/tips-for-saving-cold-damaged-plants.htm
https://www.gardeningknowhow.com/plant-problems/environmental/how-to-tell-if-a-plant-is-dead-and-how-to-recover-an-almost-dead-plant.htm

Yes, you can take cuttings. Here is an article that you may find helpful: https://www.gardeningknowhow.com/ornamental/shrubs/butterfly-bush/propagating-butterfly-bush.htm

While you do not have to remove the seed pods, you can, and it will improve its overall appearance and promote healthier blooming. It is really up to the individual gardener.

It has transplant shock. This article will help:
https://www.gardeningknowhow.com/plant-problems/environmental/learn-how-to-avoid-and-repair-transplant-shock-in-plants.htm