As far as I know, you cannot get any accepted cultures other than what is pre-determined by the game files for your nation. This game has really absurd, stupid and silly restrictions in every spot. You cannot get Russian culture as an acceptable culture as Italy, for example. No matter if you own entire Russia and 80% of your population is Russian.
POP Demand mod fixed that through events I think, but then I don't play that mod (because stupid state boundaries) so I am not sure.
Citizenship policy only affects who gets to vote, politically. Residency means only your official culture population can vote, limited citizenship allows accepted cultures to vote as well, and full citizenship allows everyone to vote regardless of who they are. Which is also an extremely silly thing in this game, real-life nations don't change voting rights every 5 years.
As for converting them to your culture, you'll have to get some of your immigrants there. A good strategy is to close down all your factories and let your homeland population be unemployed for a while, and if they are not angry they'll immigrate to your colonies. Once there, original inhabitants of the region might begin to follow those people and convert to your culture.
Full Citizenship also gives a boost to the culture conversion.
A good strategy might be to just promote bureaucrats in Tunisia. The Italian bureaucrat population will slowly grow as they immigrate/convert the inhabitants.
Keep in mind though, if a nation has core in the region, some of the population will never abandon the culture of the said nation. So if you conquer Vietnam for example, you cannot convert all the people to your culture no matter how hard you try, because Dai Nam/Vietnam has cores on the land. A certain percentage always remains in core territories.