I believe what you have is a scale insect infestation and the white"sacs" you see are the egg sacs of the cottony cushion scale. It's too hot over the next week or so to use any oil based pesticide, which is usually recommended for scale treatment. You might try a very strong, directed blast of water to knock the egg sacs off. Once the weather settles down to cooler (less than 85 degrees) you can use a horticultural spray labeled for scale (there are several available). Read labels carefully and follow the instructions accurately. Once winter sets in, use oil sprays recommended for scale. Unfortunately, these insects are only really vulnerable when the females are crawling--that is the time to really eliminate them. So you have to keep at it diligently until all the "critters" are gone.

It depends on what criteria you have used to declare them  "dead". If you scrape the bark and find no green or the branches are brittle and lifeless (leaves dropped off, etc.), then remove them. But if there's any sign of green under the bark, or leaves that are still viable, the branches should be treated. Unfortunately, some of those sacs appear to have "hatched" already, so I think spraying is number one priority.