How is the proper way of pronouncing Chicago? Szikago or Czikago?
It can be pronounced both "Szikago" and "Czikago" in Poland (Czikago is older way), unless you want to pronounce it "American way", then you have "Szikegoł" or something like that.
Formally there's still advised to make difference in pronouncing them, as "h" is voiced sound and "ch" is voiceless. Of course most Poles pronounce both as voiceless sound b/c it's just easier.
Funny, but the "orthography of h and ch" if formally not an orthographic issue, but... just proper pronunciation problem. Once someone will pronounce them properly, you will have no problem to write them properly down as well ;-)
Still most Poles, when they want to pronounce the Czech word "Praha", they would probably use voiced sound "h" in it.
Because the right bank district of Warsaw is called Praga too, we sometimes use the full name for the Czech capital: "Czeska Praga" (Czech Prague).
As for the geographical names and their Polish equivalents, some of the names are just used in their Slavic forms, popular across many Slavic countries. Others are derived from their Latin forms or are made by using Polish rules for making names of cities etc.
Such names as New York/Orlean/Zealand (in Polish: Nowy Jork/Orlean, Nowa Zelandia) are made by partial Polonization of the name or its phonetic transliteration (just like English "New Delhi" for Indian "Nai Dilli").