The country/genre lists are standard, they are send from the server to all the devices. You can not edit them yourself.
However, the lists are originating from this server and here you can add and modify database entries. So in a way you an influence what is on the lists.
Also, you can add private entries linked to your username. You select your username once under settings and then the private stations are available under the favorites app.
Also you can aff any favorite from the database to your favorite lists. So these are under your control via this server.
