Thank you. No matter how many times I check, the bug doesn't appear; only players in the forum thread wrote about it, so I can't verify it myself.

You can reserve a scripted hero by temporarily placing a mod that unlocks these heroes in the data folder. Alternatively, you can create a non-scripted hero, go to players > player_number > ReservedHeroes (in the property tree), click "..." on the desired hero, and select Shared for the scripted hero.
Battle arenas are objects of type AdventureFlybyScene.

In general, I actually did it a little differently. I placed Kha-Belekh on the map, then went to the map's property tree and created an entry in ReservedHeroes for the desired player. When I clicked on ..., I found my map in the list of single maps, which contained only one file, the name of which consists of many different letters and numbers. I selected it; this is the Kha-Belekh that I placed on the map earlier. Now it is reserved for a specific player. Could it be that StartCombat doesn't recognize it because it's on the map and simultaneously reserved? Will the settings be reset if I delete it?