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No, this is not something that can really be done.

There are a few things that can cause that. The most common is cold weather. The other two are either bark borers or a fungal disease. Check the cracks for pests and treat with a fungicide, just in case the cold weather is not the cause.

It is possible. The jury is still out on whether they kill surrounding plants, but much of the research we saw indicated that the decomposing leaves caused the most problems. I would recommend removing any fallen leaves to see if that improves it, and if not, then it may be the whole tree is the problem.

Do they have any other symptoms? Also, was your area struck by the cold weather that has affected many parts of the country? It is possible that a disease got in through the trimmed areas. It can happen, but normally that would not affect other trees. Let us know as much as you can about the disease and we will try to identify it.

Additionally, the tree may have been over fertilized, particularly with phosphorus. If this is the case, it should recover, but in the future, use a fertilizer with a lower phosphorus ratio.

This article will help you:
https://www.gardeningknowhow.com/ornamental/trees/eucalyptus/propagating-eucalyptus-plants.htm

As long as you live an area where they can survive, it is fine to transplant it to the ground.