Does the game have elements of luck or feng shui?

Yes, there is feng shui in New Horizons. In a normal playthrough you would learn this through hints in the Happy Home Academy letters.

In a nutshell (spoiler ahead):

• The game checks the outermost two slots in your apartment.
• Yellow items should go to the left
• Red items to the right
• Green items to the bottom
• The overlapping fields (bottom left and bottom right) can have any of the two colors

As for the effects:

• Yellow items increase your luck with regard to Bells (e.g. how much money a resident gives you for a gift)
• Red items, for example, increase your chance of getting valuable items in the shop.
• Green items increase your Overall Luck