Learn Polish: Dyrektorka kieruje międzynarodowym zespołem. - The director manages an international team.

It is formed from the prefix między (between) and the adjective narodowy (national). In Polish, compound adjectives are written as one solid word if the first part describes or modifies the second part. You only use a hyphen when two adjectives carry equal weight, like in polsko-angielski (Polish-English).

Why are the words międzynarodowym zespołem in the instrumental case?

The verb kierować (to manage, direct, or steer) always requires its object to be in the instrumental case. Even though we use a direct object in English, in Polish grammar you are essentially "steering with" the team.

Why does the vowel change from ó in the dictionary form zespół to o in zespołem?

This is a common vowel shift in Polish declension. The ó often appears in closed syllables (syllables ending in a consonant, like spół). When you add the instrumental ending -em, the syllable structure changes to open syllables (ze-spo-łem), causing the vowel to revert to a regular o.

Is dyrektorka fully formal, or should I use Pani dyrektor?

Dyrektorka is the standard and grammatically neutral feminine form. However, in highly formal or official spoken situations, addressing someone directly as Pani dyrektor is still very common and often preferred for politeness, though dyrektorka is perfectly fine to describe her in the third person like in this sentence.