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Coral Bush is hardy in zones 10 to 12.
It is generally grown as an annual in cold climates.
You certainly can try wintering over with grow lights, though I have not found any success stories doing so with this warm loving plant.
Here is a link to refresh you on the care requirements.

https://www.gardeningknowhow.com/ornamental/shrubs/coral-plant/growing-coral-plants.htm

It sounds like your tree suffered from transplant shock after it was planted. Here is more about this common problem:
https://www.gardeningknowhow.com/plant-problems/environmental/learn-how-to-avoid-and-repair-transplant-shock-in-plants.htm

As for the light green leaves, those could be caused by insufficient light, deficiency of nitrogen or other nutrients, or overwatering. Adding some fertilizer could help. Make sure the soil is well-drained, because this plant does not do well in poorly drained or heavy clay conditions.

I would certainly agree that this is very similar to a Coral Plant or Jatropha.
I have not been able to identify this plant.
I would suggest you take this image or a leaf and flower sample to your County Extension Office.
They should be able to id this plant from your region.

https://www.gardeningknowhow.com/extension-search/
https://www.gardeningknowhow.com/ornamental/shrubs/coral-plant/growing-coral-plants.htm

I will need much more information to be able to help. What part of the tree has the dots? What is your USDA zone? This will help me to know of the environmental factors that may be responsible. Has anything changed leading up to the symptoms? Including a photo will help quite a bit as well. Please include these bits of information and I will be more than glad to help you.

It doesn't look bad. It may just need a little more light than it receives. If you are concerned with an infection starting in the soil, you can apply wettable sulfur as a precautionary measure. Here is an article for proper care of the tree: https://www.gardeningknowhow.com/ornamental/trees/jatropha/jatropha-cucus-tree.htm

It's hard to diagnose plant problems remotely without photos and detailed description of growing conditions.

I would guess shading and inadequate sunlight to that side of the plant, root rot or fungal vascular disease. Jatropha is susceptible to verticillium wilt.