Learn Dutch: Staat jouw mok op mijn nieuwe toetsenbord?

In Dutch, you rarely use zijn (to be) to describe where a physical object is located. Instead, you use a position verb like staan (to stand), liggen (to lie), or zitten (to sit). Because a mug rests upright on its base, it "stands" (staat) on the keyboard.

Since toetsenbord is a het word, why is it mijn nieuwe toetsenbord and not mijn nieuw toetsenbord?

You are right that het words sometimes drop the -e on the adjective, but that only happens after indefinite words like een or geen (for example: een nieuw toetsenbord). Possessive pronouns like mijn, jouw, and the focus of this lesson, elkaars (each other's), act like definite articles. Therefore, the adjective gets the standard -e ending.

Is there a difference between jouw and jou?

Yes! Jouw (with a w) is the possessive pronoun meaning "your", which is why it is used here to describe whose mug it is. Jou (without the w) is the object pronoun meaning "you" (as in: Ik geef het aan jou - I give it to you). Mixing these up in writing is a very common mistake, even among native Dutch speakers!