Current questions and answers regarding the map editor.

1) How do I make it so that in the Dungeon, it's not just solid black, but so that the tiles are visible? Otherwise, it's unclear how I traveled. Only objects are visible.

In the map settings, you need to temporarily set the lighting in the Dungeon to be the same as on the surface. Save and click the map reload button.

How do I rename a building and disable its core function?

You can disable the standard function of an object using SetObjectEnabled.
You can edit the text values of an object in the Shared option.

How do I make it so that a message appears on the map immediately at the beginning of the game? And in general, how do I make it so that a message appears when you arrive at a specific location?

MessageBox - a message with an "OK" button.
ShowFlyingSign - a floating message.
REGION_ENTER_AND_STOP_TRIGGER and REGION_ENTER_WITHOUT_STOP_TRIGGER - a hero enters a specific location on the map.

How do I make it so that, for example, when you approach a monster, it says something to you and joins your party, but without a notification about it?

A message when interacting with an object. Remove the object from the map. Add the object to the hero's army.

How do I make it so that an enemy hero appears on the map not immediately, but after a certain number of days?

NEW_DAY_TRIGGER - a trigger for a new day, and add an object to the map.

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More details can be found in the forum topics, in the maps created by other users.
And here are a few useful files for the map editor:
1. The necessary documentation for scripts.
2. libhomm3 scripts - simple, standard scripts similar to those in Heroes 3 (with my improvements to the base regarding morale and luck in one battle).
3. A script editor that you MUST use.

P.S. And one more thing: before you start experimenting with scripts and changing objects, create an empty test map and work there. Be prepared for long hours of testing