Learn Farsi: این یک شهر بزرگ است.

That hidden sound is the Ezafe particle! In Farsi, when you want to describe a noun with an adjective, you link them together with an "-e" sound. Since it's a short vowel, it isn't written in the Persian script here, but you must say it: shahr-e bozorg.

Why are the words ordered as "city big" instead of "big city"?

In Farsi, nouns come before their adjectives. You state the noun first (shahr), attach the Ezafe (-e), and then add the descriptive adjective (bozorg).

Does yek mean "one" or "a"?

It means both! The word yek literally means the number one, but it is very commonly used as the indefinite article "a" or "an" just like in this sentence.

Why is the word for "is" (ast) placed at the very end of the sentence?

Farsi places the main verb at the end of the sentence. While in English you say "This is a big city", the Farsi word order is literally "This a city big is."