Is settling a second village a prerequisite to the quest of getting 800 culture points when building the town hall?

Yes you can just build a town hall in your starting village and claim the 800 culture points reward. Settling a second village is not a prerequisite.

You get the 800 CP in every scenario. Everybody is using the same Residence lvl 10 (with the help of the quest) -> 3x Settlers -> Academy lvl 10 -> Town Hall pattern to fast-settle their second village these days.