Learn Russian: Это золотой ключ.

You would use the interrogative word какой (what kind of). Since ключ (key) is a masculine noun, you must use the masculine form of the question word: Какой это ключ?

How would I use the other interrogative word from this lesson, чей (whose), with this sentence?

If you wanted to ask "Whose key is this?", you again look at the gender of ключ. Because it is masculine, you use the masculine form of "whose": Чей это ключ?

Why does the adjective золотой end in -ой instead of the usual masculine ending -ый?

The ending -ой is used for masculine adjectives when the spoken stress (emphasis) falls on the very last syllable. In золотой, the stress is on the final -ой, so it takes this ending instead of the unstressed -ый.

Since ключ is masculine, why do we use the neuter word Это instead of the masculine Этот?

Here, это is acting as a standalone pronoun meaning "this is". When used to introduce something, it always stays in the default это form, regardless of the noun's gender. You would only use the masculine этот if you were saying "this key" (этот ключ) instead of "this is a key".