Learn French: Le roi dont le château est vieux a un neveu honnête. - The king whose castle is old has an honest nephew.

In English, we say "whose castle" without an article. But in French, when you use dont to mean "whose", you must still use the definite article (le, la, or les) before the noun that is possessed.

If the castle belonged to a queen instead of a king, would dont change to match?

No, dont never changes its form. It doesn't matter if the owner is masculine, feminine, singular, or plural. It would still be La reine dont le château est vieux.

Since château is masculine, why use vieux instead of vieil?

You only use the special form vieil when the adjective comes directly before a masculine singular noun starting with a vowel or mute 'h' (like un vieil homme). Here, the adjective comes after the verb est, so we use the standard masculine singular form vieux.

Why does honnête come after the noun neveu?

Most descriptive adjectives in French are placed after the noun. While there is a small group of common adjectives that go before (often remembered with the acronym BANGS: Beauty, Age, Number, Goodness, Size), honnête follows the standard rule and comes after.