Is this how it works? The more extra food I make the more people come to my country?

No. 12 people come to your country for each acre gained. 24 come for each residential built. Residential tech works as a multiplier as well as any govt bonus.

You need food to feed your people, that's it.

Oh yeah, your tax rate matters for population too. 1-tax rate is the other multiplier.

More people = less food
Also resource decay

Ty