There are two types of Hero Skills.
Active Skills that create spells in the Book of Spells.

And Passive Skills that are permanently active and inseparable from the Hero.
Passive Skills effects are described in the table.
If a Hero leaves domain, the Hero Passive Skill stops working.
Own Hero or domain where the Hero locates can be under effect of a Passive Skill.
If a Hero is Stunned, the Hero Passive Skill will not be working.