Does a hunting license allow a person to discharge a firearm or hunt anywhere in the state?

No. Most hunting seasons are restricted by area. Many portions of the state, such as the Interstate 5 corridor in western Washington and in urban areas throughout the state, have No Shooting Zones or Firearm Restriction Zones established by local governments.
Special rules apply inside state parks, federal parks, Indian reservations, and within the incorporated portions of many cities.
You must also respect private property rights. You must have permission from the landholder to hunt on private land.