Learn French: Nous cherchons la sortie, mais elle n'est nulle part. - We are looking for the exit, but it is nowhere.

The negative structure ne... nulle part surrounds the conjugated verb. In this sentence, n' goes before the verb est, and nulle part goes directly after it. It works similarly to ne... pas to mean "is nowhere" or "isn't anywhere".

Would it be wrong to include pas and say elle n'est pas nulle part?

Yes, that would be incorrect. The expression nulle part completely replaces pas. If you use both, you create a double negative that essentially means "is not nowhere".

Why isn't there a word for "for" after cherchons?

The French verb chercher inherently means "to look for" or "to search for". Adding a preposition like pour is a common trap for English speakers. You simply place the thing you are looking for directly after the verb, as in cherchons la sortie.

Why use elle if we are talking about an exit ("it")?

Because all nouns in French have a grammatical gender, the pronoun replacing them must match that gender. La sortie is a feminine noun, so you must use the feminine pronoun elle to say "it".