All questions regarding mapmaking for Heroes of Might and Magic 3: The Shadow of Death.

Can anyone help me? How do I create a hero without a castle so that he doesn't die after a week?

Try setting "special defeat conditions" ("normal condition" is "lose all cities and all heroes").
But in general, why do you need this? What's the point of this idea?
Let the hero capture a city and live there.

If the hero is an enemy, then do the opposite.
You need to set "special victory conditions" - "defeat a specific hero".

But keep in mind that "special victory conditions" and "special defeat conditions" do not work together!
You need to set one or the other.