Learn French: J'ai éteint la lumière avant de quitter la chambre. - I turned off the light before leaving the bedroom.

The phrase avant de means before doing something. Whenever the same person is doing both actions—here, you turned off the light and you left the room—French uses avant de plus the infinitive verb (quitter). You cannot use avant que here because the subject has not changed.

Why is the French verb an infinitive (quitter) when the English translation uses an -ing word (leaving)?

In French, prepositions like de are almost always followed by an infinitive, not a present participle (an -ant word). So instead of translating the English -ing ending literally, French structures it as before to leave (avant de quitter).

Could I use partir or sortir instead of quitter in this sentence?

You need quitter here because it is followed directly by the place you are leaving (la chambre). Partir means to leave or depart in a general sense and cannot take a direct object. You could use sortir (to go out), but you would need to add the preposition de: avant de sortir de la chambre.

I do not recognize éteint. What verb is this?