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Expanding means getting new tiles. You need locally generated culture for that.
Growing means getting new population (pop) that can work your tiles for income. Dependent on the current number of population, you need to accumulate a certain amount of food to get the next pop. Your food surplus is added each turn to the accumulated food. If you haven't sufficiently housing you get a 50% (or even 75%) penalty on your surplus.
You can see the details for each city concerning the food and housing (and amenities etc. etc.) if you click on the city you're interested in and then the leftmost icon at the top of the city info on the bottom of the screen.
1) Culture = gain tiles faster
2) Food surplus = gain pop to work tiles
3) Housing = grow city size i.e. from size 1 to 4.
I always assumed that all pop was related to city size, and that all city size minus 1 could work tiles.
I think I misunderstand what you are trying to tell.
Then there are penalties to slow growth from culture, this is the housing. When I have too few housing, the growth is slowed, and this makes it so that I dont make optimal use from culture, and gain tiles less fast.
Is this how it works?
Culture unlocks new tiles for a city. You can also buy new tiles with gold. You can't work a tile that isn't unlocked, but you can have more or less tiles unlocked than you have population to work tiles.
Food supports existing population in a city, and surplus food (more food produced than consumed) grows population. The more surplus you have, the faster your city grows. Housing is an additional limiter on growth: If you have enough housing for your current population then you grow normally. If you don't have enough housing for your current population then you suffer a penalty to your growth rate (ie the surplus food you produce in that city) which slows your growth down until you get enough housing to support your population.
There's no connection between those two systems. Food and housing don't affect tile unlocks, and culture doesn't affect population growth rate or city size.
You should be able to work one tile for each population in your city. So if your city is size 6, you should be able to work up to six tiles. Note that the center tile of your city is worked for free... so it would be more accurate to say that you can work "population + 1" tiles, where one of those tiles is always the center tile.