Yesterday we've camped in a campsite near Lake Wenatchee. We've brought in a lot of wood but I've also seen numerous dead trees lying around in the surrounding forest. Is it okay to take branches from those dead trees to feed a campfire?
Do not bring in firewood. From the Nason Creek Campground page:
Don't Move Firewood: Please protect Pacific Northwest forests by preventing the spread of invasive species. Firewood can carry insects and diseases that can threaten the health of our western forests. You can make a difference by obtaining and burning your firewood near your camping destination. Visit Dontmovefirewood.org for further information.
The linked site has a lot more information about how to supply firewood for a campfire.
But please, do not start any campfire during a burn ban.