Basically, when
the player captures an AI city that has none of the player's city culture inside it, the following occurs:
The buildings with a
100% chance to survive the AI city being conquered by the player <100 iConquestProb> are
ALL world wonders, religious shrines, and the Great People buildings Academy and Scotland Yard.
The buildings with a
66% chance to survive the AI city being conquered by the player <66 iConquestProb> are
all the regular buildings the city can normally build.
The strange one out is the Greek Odeon which has a 0% chance to survive unlike the Colosseum, Ball Court, and Babylon Garden which are all 66%.

The buildings with a
0% chance to survive the AI city being conquered by the player <0 iConquestProb> are
ALL National Wonders, Wall, Castle, Barrack, Stable, Airport, Monument, Public Transportation, Library, University, Theatre, Odeon, Temple, Monastery, and Cathedral.
Now, what can the spread culture mission do for these odds?
If the AI has 100

in their city, then the Spread Culture mission can spread 5

or 5% into AI city.
So the AI city would have 100 AI

and 5player

The culture percentage would be 4.76% player / 95.24% AI
It seems to round down for the player, so it is actually 4% player / 96% AI?
When the AI city gets conquered by the player,
the occupation revolt timer is: (Thanks
Pollina!)
Code:
if (iTeamCulturePercent < GC.getDefineINT("OCCUPATION_CULTURE_PERCENT_THRESHOLD"))
{
pNewCity->changeOccupationTimer(((GC.getDefineINT("BASE_OCCUPATION_TURNS") + ((pNewCity->getPopulation() * GC.getDefineINT("OCCUPATION_TURNS_POPULATION_PERCENT")) / 100)) * (100 - iTeamCulturePercent)) / 100);
}
Turns until conquered city comes out of revolt = Floor[Floor[(3+Population*0.5)]*(100 - PlayerCulture%) / 100].
Population is the city population after the conquest. (population goes down by 1 during a city capture unless the city is already at Size 1. If a city has never been higher than Size 1, then it would autoraze unless "no city razing" was picked before the game started)
PlayerCulture% is the ratio of the player's city culture in the target city / Total culture in the target city (AI+human player).
If the player ran 6 spread culture missions in an AI city with 20 AI city

, then PlayerCulture% = 6/26 = 0.230769 = 23%
Plugging into the above formula, the number of turns of revolt in the conquered city would be Floor[Floor[(3 + Population * 0.5)] * (100 - 23) / 100].
If the population of the conquered city was a staggering 98 after conquest, then the turns of revolt would be Floor[Floor[(3 + 98*0.5)] * (100 - 23) / 100] = Floor[Floor[(52)] * (77) / 100] = Floor[52 * 77 / 100] = Floor(40.04) = 40 turns.
World builder proves this to be correct.
Now some buildings can never, ever, under any circumstances be captured when a city is conquered.
The have <bNeverCapture> = 1.
These are Monument, Library, University, Theatre, Temple, Cathedral, Monastery.
Once
PlayerCulture% equals or goes above 25% in the target city, the player
loses the ability to Raze the captured city.
Once
PlayerCulture% equals or goes above 50% in the target city, the player
no longer loses 1 population when capturing the city and
100% of ALL buildings besides Monument, Library, University, Theatre, Temple, Cathedral, Monastery(<bNeverCapture> = 1)
survives!
That means Walls, Castles, and even National Wonders (not Palace) remain in the city!

Once
PlayerCulture% equals or goes above 75% in the target city, the player gains immediate control of the city and has no turns of resistance!
Having PlayerCulture% at 49% resulted in the total destruction of 10 National Wonders and Barracks+Walls+Castle in multiple tests, so it appears the odds of buildings surviving only change at PlayerCulture% reaching 50% or higher.
Not sure how people have been capturing Heroic Epic without significant spread culture missions or losing a city with a lot of city

to the AI and conquering it back much later with National Wonders in it.
Starting with 0 player city culture in the target AI city:
It takes roughly 8 spread culture missions to get to 27% PlayerCulture%.
It takes roughly 16 spread culture missions to get to 52% PlayerCulture%.
It takes roughly 30 spread culture missions to get to 75% PlayerCulture%.
Gifting a city away does not remove the player's city culture.
Only the player's plot culture on the city square and surrounding 8 squares vanishes.
Giving a relatively new Size 2 city away with 0

and immediately reconquering it acts like 0 PlayerCulture%, destroys buildings, and gives 3 turns of resistance.
So make sure to put 1

into it before doing something like that.