"Istanbul is the biggest city in Turkey."
Translation:İstanbul Türkiye'deki en büyük şehir.
"şehir" is one of many loan words (mostly from Arabic) that lose their second vowel when you add a suffix that starts with a vowel. This only occurs in a few loan words and some words for body parts and have to be memorized as you learn them. They will always have just two syllables.
In other sentences, the word with "ki" suffix went first, before the noun. "Hastanedeki çocuklar...", "Parktaki kadın...", etc. Why is it different here? The noun goes before the word with the "ki" suffix. On the other sentences it doesn't accept it if I change the words so that the noun comes first.
I am not sure what you are asking. In this sentence, -ki (just like in the two examples you provided) makes a subordinate clause in English. "Türkiye'deki" would mean "that is in Turkey" and it modifies the noun "şehir" which just so happens to have some adjectives before it. :)