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Is the black powdery or soot-like in nature? It could be sooty mold, which is often an indication of pests. I would treat it with neem oil to both rid the plant of the pests and sooty mold problem.

It should be ok to go ahead and transplant now during spring, but just be sure to keep it well watered. This article will give advice to help avoid transplant shock: https://www.gardeningknowhow.com/plant-problems/environmental/learn-how-to-avoid-and-repair-transplant-shock-in-plants.htm

Sap is normal following pruning and will eventually stop on its own. Make sure to give it some extra water and fertilizer to help keep its health up. But as long as the vine looks ok overall, I would not worry too much. If it makes you feel more at ease, you can treat the vine with Neem oil, which is a safe and effective fungicide/insecticide that should help guard against these issues while it heals. For future reference on pruning, this article will help: https://www.gardeningknowhow.com/edible/fruits/grapes/pruning-muscadine-grapes.htm

I can't tell you what's killing them, but I can give you some ways to evaluate the situation, possibly figure out what the problem is, and where to go for analysis.
The first thing is to look at the maintenance of the grapes, to see if they are missing something that they need. Plants that are healthy are much less likely to contract disease, so it follows that a sickly plant may well have some cultural deficiency. https://www.gardeningknowhow.com/edible/fruits/grapes/growing-grapevines.htm
After that, look at the leaves, the stems, the soil for descriptions of common diseases and pests: https://www.gardeningknowhow.com/edible/fruits/grapes/treating-grapevine-problems.htm
If you still don't clearly see the problem, take some samples of leaves, stems and soil to the nearest county extension service, where they will be able to advise you. This link will help you locate the nearest one: https://www.gardeningknowhow.com/garden-how-to/info/what-is-extension-service.htm

Muscadine is pretty resilient and it will regrow, even if cut to the base.

Here is a link to an extension article that might interest you on propagating muscadine vines from cuttings: https://bit.ly/1JH3lsC

For more information on the care of muscadine grapes, please refer to the following articles:
https://www.gardeningknowhow.com/edible/fruits/grapes/pruning-muscadine-grapes.htm
https://www.gardeningknowhow.com/edible/fruits/grapes/muscadine-grapevine-planting.htm

Yes, here is an excellent article.
The last paragraph will pertain to your circumstance.

https://www.gardeningknowhow.com/edible/fruits/grapes/pruning-muscadine-grapes.htm