Learn German: Dreh den Schlüssel!

This is the informal singular (du) command form (imperative). To make it, you take the present tense du form (drehst) and drop the -st ending and the pronoun. Adding an -e to the end (Drehe) is also grammatically correct but usually dropped in everyday spoken German.

Why is it den Schlüssel and not der Schlüssel?

Schlüssel is a masculine noun (der Schlüssel). Because the key is the direct object receiving the action of being turned, it takes the accusative case, changing der to den.

Given our current lesson on r- forms, could I use rumdrehen here?

Yes! While drehen works perfectly, you will often hear native speakers use the separable verb rumdrehen (a colloquial, shortened version of herumdrehen or umdrehen) for turning a key in a lock. You could say Dreh den Schlüssel rum! to mean the exact same thing.

Could I use drehen if I want to tell someone to turn left or right?

No, drehen is strictly for rotating something on an axis (like a key, a steering wheel, or your body). To tell someone to turn left or right while walking or driving, you must use the separable verb abbiegen.