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You can plant it, and keep it watered until you see new growth. After you see that it has taken to its spot, then you can begin to prune it. This article will give you more information: https://www.gardeningknowhow.com/ornamental/flowers/duranta/care-of-duranta-plants.htm

15-25 feet tall.

It isn't necessary to prune these after flowering, but you may do so if you would like. Just prune back a few inches of the tips to cut of only the flowering areas. This article will give you more information on the care of these: https://www.gardeningknowhow.com/ornamental/flowers/duranta/care-of-duranta-plants.htm

It looks like the start of a fungal infection. I would add dolomitic lime and wettable sulfur around the area. This will stop the infection, and bring the pH back to normal after the fungus is killed. This article will give you more information on the care of these: https://www.gardeningknowhow.com/ornamental/flowers/duranta/care-of-duranta-plants.htm

Yes, as long as it receives some direct sun. They can tolerate some shade, but they do best with full sun exposure. I think it would do just fine in the described location, though.

This article will give you more information on their care: https://www.gardeningknowhow.com/ornamental/flowers/duranta/care-of-duranta-plants.htm

Duranta need loamy and well draining soil. It sounds like your clay soil is not suitable for your plants.
The black leaves are likely due to die off.
Further amendment would be needed to support healthy Duranta growth.

https://www.gardeningknowhow.com/ornamental/flowers/duranta/care-of-duranta-plants.htm