Hi, yes you're correct in both cases - you can say London's parks/the parks of London (more often you would say "the parks in London" but your statement is still correct).
Two minor corrections in the wording of the question:
The title should say: "Should city names take apostrophes?" or you could also say "Should the names of cities take apostrophes?"
In the main body, you wrote "Do I also have to use it when mentioning cities´names, countries´, towns´, continents´" Here you need to see city as an adjective for the noun "name", so you would say "Do I also have to use it when mentioning city names, country names, town names or continent names" Or more naturally, "when mentioning the names of cities, countries, towns or continents.
I hope that's clear, let me know if you have any other questions!