Learn Dutch: Behalve de lichaamstaal is ook de mimiek erg belangrijk. - Besides the body language, the facial expressions are also very important.

You are right that behalve often means "except" (excluding something). However, when it is paired with ook (also) later in the sentence, the meaning shifts to "besides" or "in addition to" (including something). The presence of ook is your clue that body language is being included, not excluded.

Why is the verb is placed before the subject de mimiek?

This is an example of inversion. The sentence starts with the prepositional phrase Behalve de lichaamstaal. Because this phrase takes up the first position in the sentence, the verb is must take the second position, pushing the subject (ook de mimiek) to the third position.

Why is mimiek singular when the English translation uses the plural "facial expressions"?

In Dutch, mimiek is generally used as a singular, uncountable noun that refers to the collective movement and expression of the face. You do not pluralize it to talk about multiple expressions, unlike the English phrase "facial expressions."

Could I use naast instead of behalve here?