How can I sort the cities displayed on the home page? Or how can I add some specific city on the homepage?
For information, the cities in the homepage are sorted by "population" column in the database. So you if you want add a specific city there, you have to enter a big value for the "Population" field by editing the city from the Admin panel -> Setup -> International -> Countries -> Cities.
NOTE: You can check the Population value of the first city displayed on the homepage to know how value you can enter for your other specific city.