Cottonwoods are relatively short-lived trees that do little to protect themselves from insect and disease attack. Couple that with their fast growth and weak wood and you have a tree that does not go gracefully into old age. Dead branches can be due to shading from other branches, and attack by poplar borer or other borers, but a very likely cause is a fungus called a canker that girdles stems or the trunk. The only thing you can do to counter any of this is to avoid injuring it and to give it plenty of water to keep it vigorous. You should begin to think about what is going to replace it, though, since it will continue to have these problems and they will get worse with age.

Can anything be done if it has borer or canker? Should the dead limbs be removed?

Water is the oval thing that will help with cankers. You can't keep them out; just help the tree compete with them once they are in there. Borers also can't be dealt with once they are in there, but insecticide can be used to try to keep them out. The treatment is Sevin insecticide sprayed on the trunk and on any branch you wouldn't want to lose. Most likely it would have to be done yearly in mid- late-spring. It will take high pressure spray equipment so you will have to have it done. In a tree that big it will be expensive and you will bother some of your neighbors. Yes, you should prune out dead branches that are big enough to hurt someone if they fell. Otherwise it doesn't matter.

Can any supplement feedings  along with water to the roots help the tree cope? Removing the dead limbs does not slow down borers or cankers? The dead branches don't take any vitality from the tree itself?

Fertilization does not help and can hurt, since it can over-stimulate growth. Trees usually don't need fertilization. With some diseases (like fireblight) it is important to remove branches that have been killed and to get rid of them to keep from spreading the disease. But with cankers and these kinds of borers it doesn't matter.

Thanks for informed advice. I appreciate your patience. I hate to think of losing this beauty that I planted as a sapling so many years ago. It is good to be forewarned to make plans.