I have two more questions. Actually I am pretty surprised nobody has dropped the answers yet... But maybe there is a reason for that, I am unaware of.
It seems obvious to me, that there are cutoff points with barbs, the three most relevant seem to be
1) animals disappearing (no longer have to worry about barbs moving 2 tiles)
2) barbs beginning to enter your borders (before they are just roaming randomly)
3) barb galleys appearing (not sure if there is also a grace period before they enter you territory)
I assume that these cut offs are fixed, not dynamic, so does anyone have an overview? Just to explain why I want to know:
Before 1 fog busting is completely irrelevant, before 2 you don't have to worry about garrisons and before 3 you don't have to fog bust coastal tiles.
Someone should really write a complete guide on barbarians one of these days.
Most of your questions are answered in this guide here:
https://forums.civfanatics.com/threads/barbarians.324961/
1) Animals start spawning between Turn 5 and Turn 6 on all game difficulties.
They spawn later and in smaller numbers on easier game settings.
They start to vanish 1-animal-per-turn once both of these conditions are met.
1st Condition: The average number of cities in the world per civ (including the human player) is greater than 1.5 cities.
So a standard map with 6 AI will reach this point once the world has 11 cities. (Barb cities don't count)
2nd Condition: A certain number of turns have elapsed based on game difficulty and game speed.

So on Deity difficulty, the first animals will appear on Turn 6, and will begin vanishing one at a time starting on Turn 11.
This frees up room for barb Warriors and barb Archers to spawn in the vacant areas they leave behind as soon as Turn 11.

(Thanks
Anysense!)
Animals are more limited than normal barbarians.
When wandering the wilderness, they will not move onto resources such as wheat or dye or even bronze which you don't have the tech to even see yet.
But if they see a Worker or Settler or player Scout on that resource, they will pounce and kill!
Thankfully, animals are not capable of entering player borders under any circumstances.
If you settle a city next to an animal and get them inside your borders on purpose, their only valid move is to move out of your culture.
Once I pinned a bear next to a mountain range doing this, and he was stuck there until he vanished.
Animals are also nice enough not to stack up like regular barbs can do.
Imagine 2 bears on the same tile.
2) Regular barbs start entering your borders for only 2 reasons in my experience.
One is to kill something.
A warrior or settler or worker standing on the edge of your borders is going to get killed if a barb archer or warrior is standing next to them.
Non-animal barbarians don't care about borders if they can immediately kill something.
The second is when the average number of cities in the world exceeds 3.
Like a switch, the barbs go from wandering to charging directly at cities and murdering everything.

On a standard map with 6 AI, this occurs when the world gets its 22nd city.
I know
DanF tends to be right 100% of the time

, even about arcane STRIKE knowledge, but I just have not seen this kind of behavior.
Make a test game, give everyone 2 cities, then add 1 more city.
Put improvements on every city tile and then surround the city with barbs and press next turn.
They all just ... leave.
All the border improvements remain unmolested until the NumCities > 3*NumPlayersAlive threshold is breached.
The barbs go crazy until a few barb cities get founded and then they calm down again.
**Edit 2**
Huh, I've run a few more tests and now I'm seeing the barbs
are a bit more aggressive when
DanF's 1st threshold NumCities > 2*NumPlayersAlive threshold is breached.
About 1/3rd of them seem to gleefully cross the border now to pillage when a standard game with 6 AI reaches 15 cities.
Are barbs placed with world builder defective somehow and take some time to fix their AI scripts?
3) Barb galleys?
Deity barbs start with Hunting, Archery, The Wheel, Agriculture, and 1

per turn.
On a standard map with 6AI and a human player, they gain 1% of any tech per turn that 3 civs know.
Once 5 civs know the tech, they gain 2% of it per turn.
Once all 7 civs know the tech, they gain 3% of it per turn!
The math says you can breathe easy if only 2 of the 7 civs know a tech.
They can also found cities to slightly bump up their tech speed, but for the most part they are gaining

in multiple techs each turn that most everyone already knows.
I would say that as soon as 5 out of 7 civs know Sailing, the barbs will have Sailing in 50 turns max and then start spawning barb galleys.
**Edit**
LowtherCastle used to advocate the knowledge of how many barb city population there is on a map.
Press F8 at any time to see the total population of the civilized world.
Click the Resolutions button.
If it says a vote requires 13 out of 27 votes, that means the civilized world has 27 population.
Then press the Victories button (Also inside the F8 Victory Conditions menu)
Go to the % population dom limit the human player has.
That % number is how much the player population has compared to the world total population PLUS barb population.
================
Let's say there are 5 votes in the world on Turn 1 of a small map.
There are 5 population in the world when all the civilized civ's add up their city populations.
The Victory button says the player (1 population) has 20% of the world's population.
That means there are no barb cities.
If the player has 16.66% of the world's population, that indicates the player has 1 pop, the 4 AI have 1 pop, and the barbs have 1 pop.
By comparing the % population dom in the victory tab vs. the member votes in the resolution tab, it is possible to monitor the barb city population at any moment in the game.
Barb cities tend to indicate that the onslaught of barbs after the >3 cities threshold will be winding down and stopping.
Barbs like to found cities in spots with lots of resources that nobody has direct vision on.
It is a bit crazy that barb cities can affect domination victories so blatantly, but it has already been a factor in one major SGOTM tournament.
