It looks like characters do not give fear immunity to their unit in 8th. Look at the last paragraph of the fear rules (pg 69). It says that Fear-causing models do not suffer if their unit fails the Fear test. If the unit had to take a Fear test, they must not be immune to Fear. Also, the Character rules on pg 100 say that Character special rules don't apply to the unit unless specifically stated.
It also specifies that only units in base contact with a Fear-causer have to take a test. Does this mean that a Skrox unit won't cause Fear since the Krox won't be in base contact?