How much humidity is being maintained in cabin and cockpit of B787?
These sources say that most airliners maintain a humidity of 4-7%, while the 787 maintains 10-15%. Of course these values can vary with conditions, and other sources put them lower or higher.

The cabin and cockpit will not have very different air qualities. While some cockpits may humidify the cockpit air slightly, the cockpit tends to have a greater amount of circulation, leading to drier air than the rest of the cabin.