It’s a bit embarrassing, but I don’t know how to use the map editor; I didn’t think it was necessary.

I don’t see anything embarrassing about that :) Besides, you haven’t been playing for that long, so it’s something you can learn ;)

1. We play large maps with Andrey, sometimes for several days. Can he give himself some artifact after the game has already started (for example, when I’m not around)?
2. What formula is used to calculate damage?
3. Does the hero’s development depend on his background (if you take heroes from the same Castle with the same initial abilities)?

1. No, he won’t be able to change anything once the game has started.
2. Each unit has a certain amount of health points (HP). The enemy unit has a certain attack power (minimum and maximum). All of this is displayed in the unit panel. So, he starts attacking your unit, and its health points gradually decrease.
3. Are you asking if they will be offered the same skills? Then, no. It seems like a random selection is used here.

General request: I need some tips. Example (I apologize, the idea is someone else’s, but it’s your “Magic of Order. Combine moving enemy archers to your side and hypnotizing them”).

You need to upgrade Order first. You are playing as Nature. But if you have time, after you fully upgrade the Druid, you will have to decide who to upgrade next. It’s better to think about this.
By the way, against Chaos, it’s better to build Phoenixes and cast all the blessings that Nature has on them (or at least the most important ones); then you won’t be inferior to Chaos Dragon.