My coconut plant as turned brown and collapsed. It's in a greenhouse and watered. Is it dead?
These are not long-lived plants. This article should answer your questions: https://www.gardeningknowhow.com/edible/fruits/coconut/growing-coconut-palm-trees.htm
I read your article on soaking it in water for 2-3 days, etc. but does the coconut have to be BROWN first? Or can I do that while it's green, just off the tree? Should I wait for them to fall off the tree? Or can I cut them down and plant them?
You need to use a coconut that has turned brown. The coconut is a seed, and like any seed, it needs to ripen before it can germinate. It's not ripe until the husk is brown.
I have had two coconut palms in the front yard for about 7 years. Recently, I have noticed a sap residue on my auto whenever parked under the palms and then a deposit on other plants under the branches. It is like a black sticky soot and has discolored the leaves. The palm itself has all the branches turned blackish and most of the green is gone. It is still producing coconuts and new growth.
It sounds like sooty mold, which is caused by fungus growing on the sticky substance (honeydew) exuded by insects such as aphids, scale, or whitefly. This is relatively easy to get rid of by controlling the insects. Neem oil helps with both. Read more here: https://www.gardeningknowhow.com/plant-problems/disease/how-to-get-rid-of-sooty-mold.htm
https://www.gardeningknowhow.com/plant-problems/pests/pesticides/neem-oil-uses.htm
How can I grow a coconut palm so that its trunk is angled (or "dancing" as we say in Belize)?
These palms are the product of some major force, like wind or water, that has partially knocked over the plant. Most of the root structure remains connected, so the plant can continue to grow, although it's tilted, or even lying on ground. So if you want to force a plant to do this, you become the "major force." You can start with a plant that has some growth to it, and by shoveling the soil away from the roots on one side and under the roots on the other side, you can maybe push it over somewhat. Or you can plant a palm so that it is tipped at the angle you want. Or you can start with a young palm, and force it to grow tilted by staking, weighting, and tieing.
My coconut tree is day by day going on dying from insects.
Can you identify or describe the insects? Can you describe what is happening to your tree? Answers to these questions will help me better assist you.
In the meantime, I can offer you a great article on the reasons coconut trees die, which will help you:
https://www.gardeningknowhow.com/edible/fruits/coconut/coconut-tree-problems.htm
We have six large yellow coconut palm trees and they all are black on one side of their trunks, and have a lot of small holes in them.
I suspect that this is "stem bleeding" which is discussed in the following extension article:
https://bit.ly/1cX7ApH
Can I have only one Coconut tree in the garden?
Yes, you can grow one coconut tree. This article will help: https://www.gardeningknowhow.com/edible/fruits/coconut/growing-coconut-palm-trees.htm