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

In the map editor, there is a "Hero Camp" – this is where the hero from the previous map transitions to. Depending on their number on the next map, as far as I remember, it determines the number of heroes that will transition. What is carried over is defined in the campaign editor. In the "Hero Camp" itself, it is determined which specific hero it will be.

Yes, in the campaign editor, in the starting settings, you need to specify the previous map of the scenario.