A program for calculating the strength of the guard on random maps in Heroes of Might and Magic III, called H3CalcGuards.

1. Does the bug duplicate everything, or only all objects with guards? I mean, if there are 2 outposts or 2 stables, does that mean there will be twice as many loot piles/campfires/chests?

The bug isn't that the objects are duplicated. It's possible for 2 identical objects to be generated in the same group (except for objects with impassable triggers, like a prison or a tavern). The bug is that while the group is being populated, the game doesn't "know" about the objects that have already been added to it, which is why it might add a second outpost to the group, even though there's a limit of 1 per zone.
The fact that 2 guard towers sometimes generate next to each other under the same guard is normal; it's a standard situation.

2. The critical consequences are different. I managed to get out of a treasure map on a small map with 100+ ducks by taking 6 drowned. I doubt anyone would bother exploring rocks or even libraries after that.

Well, it was just a really good treasure map; it's unlikely to be a bug. It's random, and it would be strange if, after so many years of Heroes, such a thing hadn't generated even once. :)
By critical, I mean consequences that lead to incorrect game behavior or even crashes.

4. Is it true that the guard for a duplicated object will guard only one of them?

No. Since the "duplicated" objects are added to the group using the standard algorithm, they are counted as 2 separate objects in the group's value.

5. How can you tell the difference between a regular "shlak-art" and a quest "shlak-art"? The guard is sometimes visible from a distance, but it's hard to tell on a guard worth 5k.

The value of a regular treasure artifact is 2000. A quest artifact can also be 2000, so it's unlikely you'll be able to tell the difference based on value (but each seer has a frequency of 10, while a random artifact of each level has a frequency of 150, so in the case of a small guard, it's more likely that it's just a regular artifact).
Quest artifacts are also banned at the start of the map, which means they exist in the game in only one copy and don't appear in dungeons, the market, etc. If an artifact that is exactly the same has already appeared in the game in some way, then this one is definitely not a quest artifact.
You can also analyze the location of the seers' huts (although this is already a murky business). After placing an artifact, the game tries to place its hut one zone away; if that's not possible, it tries two zones away, and so on. If it's not possible to place it anywhere else, it goes to the next zone, and an artifact and its hut can never be in the same zone under any circumstances. Therefore, if the surrounding zones have been explored, and there are no huts visible except in the adjacent zones, it's likely that there are no quest artifacts in that zone.

6. Is the player's home town counted when determining the guard's strength?

No. The number of zones is counted, not the number of towns. The zones that are counted both in the total number of zones with towns and in the number of zones with a specific town must meet the following condition:
- There must be at least one checkmark in the Town types graph for the zone.
It doesn't matter whether a town actually appears there or not.