Current questions and answers regarding the map editor.

Well... for example, I put a hero on a map, changed his shared data, and now he looks like a druid. If I upload this map to the internet, will he look the same there too?

Exactly.

And also - if I then create a new map and put this hero on it, he looks normal again, but when I launch the game, he still turns into a druid.

Yes, that's also true.
Here's how it works. When the game starts, it searches for all zip archives with a specific extension in certain directories. First, it scans the data folder and loads all archives with the .pak extension from there. Then, it goes to the Maps folder and loads .h5m archives. Similarly, it does the same in UserMODs; I believe it loads all archives from there, regardless of the extension, but it definitely loads .h5u archives. If two files with the same name are loaded, the newest one (with the creation date closest to the current date) is used in the game. That's all there is to it. Therefore, if your map is in the Maps folder, it will be loaded into the database when the game starts, and all the mods from that map will be applied everywhere.