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You will be fine to do so. It would not hurt to do it now. It is good to make sure that they are in a well lit area, as lack of light can cause this.

Yes, trees with larger root systems such as this should not be placed neat features that may get damaged. I would recommend finding a different spot at least 40 or 50 feet away from the dam.

This is tricky. The growth will not recover, but if it is cut, then it may not shoot new growth. It would be best to leave it until you see what will grow back and what will not. After a few months, you can then cut the dead growth off. Often, they will replace some of the growth, but not usually all of it.

Russian Cypress, like most evergreens, doesn't usually need fertilizer once it's established, unless it appears to have a deficiency (like if leaves turn yellow). Optionally, it can be fertilized once a year with a fertilizer designed for evergreens.
http://www.extension.umn.edu/garden/yard-garden/trees-shrubs/fertilizing-evergreens-conifers/

Water deficit = drought stress? Fungal disorder? Beetle-borer or mites? Need more information, geographical area, growing conditions, irrigation program, species identification, photos.
Do you have a local nursery that might help. They are usually helpful for ID of trees and shrubs in the area and common disease and pest problems. Do you have a county/university cooperative extension service with an advisory service? Or pay for a professional consultation with a local arborist or landscape advisor.

Can you include photos? Has your area experienced random cold snaps between the warmth? This can cause the temporary issue. If it comes out of it easily, then I would suspect that it is just an environmental issue that the tree is equipped to handle.