Learn French: Le vieux château a cent fenêtres. - The old castle has 100 windows.

Numbers generally do not change to match the plural noun. The word cent only takes an "s" when there are exact multiples of a hundred (like deux cents for 200). Since there is only one hundred here, it stays as cent.

Why does vieux come before château? I thought adjectives go after the noun.

Most do, but a small group of common, short adjectives describing Beauty, Age, Goodness, and Size (often called BAGS adjectives) go before the noun. Because vieux means old (Age), it comes before château.

Do I pronounce the "t" at the end of cent when reading this sentence?

No, the "t" here is silent. You only pronounce the "t" in cent if the following word begins with a vowel sound, to link them together. Because fenêtres starts with a consonant, the "t" stays silent.