I dunno what "people" do, but I know what I do
1. Depends somewhat on nation. My favorite for instance is Vanheim - and when playing them I make a Vanjarl my prophet so that I can have one commander with access to Fanaticism and Divine Blessing. Of course Vanjarls are stealthy, so in terms of your question I'm getting it both ways. But I don't use him as a stealth preacher, but to lead an army of Vans and Valkyries.
2. I don't believe his priest level has any effect on his dominion spreading, unless you are using him to preach. Then it does have an effect.
3. Yep, using his priestly powers to support you army is IMHO the way to go.