RTW Factions
In Rome Total War their are a number of factions that you can play plus a small number that you cannot, below is the list of factions with the related cultures.
Culture has an effect on public order when your factions culture is different to the settlements and it's buildings.
Culture Penalties that would be applied
Culture penalties work in two ways
If the governors building is not your factions culture then their is a base penalty for the governors building itself plus a penalty based on the proportion of building levels in the settlement.
Such that without any of your own factions building the penalty is 50%, this being reduced as you build. Each level of a building counts toward reducing culture penalty. So the penalty is reduced if you upgrade a building over one of your own.
Destroying other cultures buildings will only affect the culture penalty if you have some of your own cultures buildings
Governors building is your own culture
This appears to be a lot simpler in that each building not of your culture applies a 1.5% penalty, there might be a few exceptions to this.
Note that some settlements have a base culture penalty applied when the original culture is not your own.